[Introduction] - Groups of Genus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Groups of Level:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
18
20
21
24
25
26
27
28
30
32
36
48
^ | Level 1 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/1Z) Matrix Generators |
---|---|---|---|---|---|---|---|---|---|
1A0 | Γ | 1 | 1 | 1 | 1 | 1 | |||
^ | Level 2 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/2Z) Matrix Generators |
2A0 | Γ2 | 2 | 1 | 1 | 0 | 2 | [ 1, 1, 1, 0 ] | ||
2B0 | Γ0(2), Γ1(2) | 3 | 1 | 3 | 1 | 0 | [ 0, 1, 1, 0 ] | ||
2C0 | Γ(2) | 6 | 1 | 1 | 0 | 0 | |||
^ | Level 3 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/3Z) Matrix Generators |
3A0 | Γ3 | 3 | 1 | 1 | 3 | 0 | [ 0, 1, 2, 0 ] , [ 0, 2, 1, 0 ] , [ 1, 2, 2, 2 ] , [ 2, 0, 0, 2 ] | ||
3B0 | Γ0(3), Γ1(3) | 4 | 1 | 4 | 0 | 1 | [ 0, 2, 1, 2 ] , [ 1, 2, 1, 0 ] , [ 2, 0, 0, 2 ] , [ 2, 1, 2, 0 ] | ||
3C0 | 6 | 1 | 3 | 2 | 0 | [ 2, 0, 0, 2 ] , [ 2, 1, 1, 1 ] | |||
3D0 | Γ(3) | 12 | 1 | 1 | 0 | 0 | [ 2, 0, 0, 2 ] | ||
^ | Level 4 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/4Z) Matrix Generators |
4A0 | 4 | 1 | 4 | 2 | 1 | [ 0, 1, 3, 0 ] , [ 1, 1, 1, 2 ] , [ 3, 0, 0, 3 ] | |||
4B0 | Γ0(4), Γ1(4) | 6 | 1 | 3 | 0 | 0 | [ 0, 1, 3, 2 ] , [ 1, 2, 2, 1 ] , [ 2, 1, 3, 0 ] , [ 3, 2, 2, 3 ] | ||
4C0 | 6 | 1 | 3 | 2 | 0 | [ 0, 1, 3, 0 ] , [ 1, 2, 2, 1 ] , [ 2, 1, 3, 2 ] , [ 3, 2, 2, 3 ] | |||
4D0 | 8 | 1 | 4 | 0 | 2 | [ 1, 1, 1, 2 ] , [ 3, 0, 0, 3 ] | |||
4E0 | 12 | 1 | 3 | 0 | 0 | [ 1, 2, 2, 1 ] , [ 3, 2, 2, 3 ] | |||
4F0 | 12 | 1 | 6 | 2 | 0 | [ 0, 1, 3, 0 ] , [ 3, 0, 0, 3 ] | |||
4G0 | Γ(4) | 24 | 1 | 1 | 0 | 0 | [ 3, 0, 0, 3 ] | ||
^ | Level 5 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/5Z) Matrix Generators |
5A0 | 5 | 1 | 5 | 1 | 2 | [ 1, 1, 4, 0 ] , [ 2, 1, 0, 3 ] , [ 4, 0, 0, 4 ] , [ 4, 2, 4, 1 ] | |||
5B0 | Γ0(5) | 6 | 1 | 6 | 2 | 0 | [ 2, 3, 3, 0 ] , [ 4, 0, 0, 4 ] , [ 4, 1, 3, 1 ] | ||
5C0 | 10 | 1 | 10 | 2 | 1 | [ 3, 0, 1, 2 ] , [ 4, 0, 0, 4 ] , [ 4, 3, 3, 0 ] | |||
5D0 | Γ1(5) | 12 | 1 | 6 | 0 | 0 | [ 2, 3, 3, 0 ] , [ 4, 0, 0, 4 ] | ||
5E0 | 15 | 1 | 5 | 3 | 0 | [ 1, 3, 1, 4 ] , [ 3, 0, 3, 2 ] , [ 4, 0, 0, 4 ] | |||
5F0 | 20 | 1 | 10 | 0 | 2 | [ 4, 0, 0, 4 ] , [ 4, 3, 3, 0 ] | |||
5G0 | 30 | 1 | 15 | 2 | 0 | [ 2, 4, 0, 3 ] , [ 4, 0, 0, 4 ] | |||
5H0 | Γ(5) | 60 | 1 | 1 | 0 | 0 | [ 4, 0, 0, 4 ] | ||
^ | Level 6 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/6Z) Matrix Generators |
6A0 | 6 | 1 | 2 | 0 | 3 | [ 0, 1, 5, 1 ] , [ 1, 2, 2, 5 ] , [ 3, 4, 2, 3 ] , [ 5, 0, 0, 5 ] , [ 5, 3, 1, 2 ] , [ 5, 4, 4, 1 ] | |||
6B0 | 6 | 1 | 3 | 4 | 0 | [ 2, 1, 1, 4 ] , [ 3, 2, 4, 3 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 1, 1 ] | |||
6C0 | 8 | 1 | 4 | 0 | 2 | [ 1, 3, 3, 4 ] , [ 3, 2, 4, 5 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 2, 3 ] | |||
6D0 | 9 | 1 | 3 | 3 | 0 | [ 3, 2, 4, 3 ] , [ 4, 3, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] | |||
6E0 | 12 | 1 | 3 | 4 | 0 | [ 1, 3, 3, 4 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 1, 1 ] | |||
6F0 | Γ0(6), Γ1(6) | 12 | 1 | 12 | 0 | 0 | [ 1, 0, 3, 1 ] , [ 3, 2, 4, 5 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 2, 3 ] , [ 5, 4, 5, 3 ] | ||
6G0 | 18 | 1 | 9 | 2 | 0 | [ 4, 3, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] | |||
6H0 | 18 | 1 | 9 | 4 | 0 | [ 0, 1, 5, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] | |||
6I0 | 24 | 1 | 4 | 0 | 0 | [ 3, 2, 4, 5 ] , [ 3, 4, 2, 1 ] , [ 5, 4, 2, 3 ] | |||
6J0 | 24 | 1 | 8 | 0 | 3 | [ 2, 1, 5, 3 ] , [ 5, 0, 0, 5 ] | |||
6K0 | 36 | 1 | 3 | 0 | 0 | [ 1, 0, 3, 1 ] , [ 5, 0, 0, 5 ] | |||
6L0 | 36 | 1 | 9 | 4 | 0 | [ 0, 1, 5, 0 ] , [ 0, 5, 1, 0 ] , [ 5, 0, 0, 5 ] | |||
^ | Level 7 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/7Z) Matrix Generators |
7A0 | 7 | 2 | 7 | 3 | 1 | [ 0, 3, 2, 0 ] , [ 2, 5, 6, 5 ] , [ 4, 0, 6, 2 ] , [ 6, 0, 0, 6 ] , [ 6, 6, 2, 1 ] | |||
7B0 | Γ0(7) | 8 | 1 | 8 | 0 | 2 | [ 3, 2, 0, 5 ] , [ 5, 3, 4, 4 ] , [ 6, 0, 0, 6 ] | ||
7C0 | 14 | 2 | 7 | 2 | 2 | [ 1, 3, 4, 6 ] , [ 2, 0, 1, 4 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] | |||
7D0 | 21 | 1 | 21 | 5 | 0 | [ 0, 3, 2, 0 ] , [ 1, 3, 4, 6 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] | |||
7E0 | Γ1(7) | 24 | 1 | 8 | 0 | 0 | [ 6, 0, 0, 6 ] , [ 6, 2, 5, 3 ] | ||
7F0 | 28 | 1 | 28 | 4 | 1 | [ 0, 3, 2, 0 ] , [ 4, 3, 5, 4 ] , [ 6, 0, 0, 6 ] | |||
7G0 | 42 | 2 | 7 | 6 | 0 | [ 0, 3, 2, 0 ] , [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] | |||
^ | Level 8 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/8Z) Matrix Generators |
8A0 | 8 | 2 | 4 | 2 | 2 | [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 4, 3, 5, 4 ] , [ 5, 0, 4, 5 ] , [ 5, 4, 0, 5 ] , [ 6, 3, 7, 1 ] , [ 7, 0, 0, 7 ] | |||
8B0 | 12 | 1 | 3 | 4 | 0 | [ 0, 5, 3, 0 ] , [ 3, 6, 6, 7 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 5 ] , [ 7, 4, 4, 7 ] , [ 7, 6, 6, 3 ] | |||
8C0 | Γ0(8) | 12 | 1 | 6 | 0 | 0 | [ 1, 4, 4, 1 ] , [ 3, 0, 0, 3 ] , [ 4, 5, 3, 2 ] , [ 5, 4, 4, 5 ] , [ 7, 2, 6, 3 ] | ||
8D0 | 12 | 1 | 6 | 2 | 0 | [ 0, 5, 3, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 5 ] , [ 7, 4, 4, 7 ] , [ 7, 6, 2, 3 ] | |||
8E0 | 16 | 1 | 4 | 0 | 4 | [ 1, 1, 5, 6 ] , [ 1, 4, 4, 1 ] , [ 5, 0, 4, 5 ] , [ 6, 3, 7, 1 ] , [ 7, 0, 0, 7 ] | |||
8F0 | 16 | 1 | 16 | 4 | 1 | [ 0, 1, 7, 0 ] , [ 0, 3, 5, 0 ] , [ 2, 3, 3, 5 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] | |||
8G0 | 24 | 1 | 3 | 0 | 0 | [ 1, 2, 0, 1 ] , [ 1, 4, 0, 1 ] , [ 1, 6, 0, 1 ] , [ 3, 2, 0, 3 ] , [ 5, 4, 0, 5 ] | |||
8H0 | 24 | 1 | 6 | 4 | 0 | [ 0, 5, 3, 0 ] , [ 1, 4, 4, 1 ] , [ 5, 0, 0, 5 ] , [ 7, 4, 4, 7 ] | |||
8I0 | Γ1(8) | 24 | 1 | 12 | 0 | 0 | [ 3, 2, 6, 7 ] , [ 4, 5, 3, 2 ] , [ 5, 4, 4, 5 ] , [ 5, 6, 2, 1 ] | ||
8J0 | 24 | 1 | 12 | 0 | 0 | [ 1, 2, 4, 1 ] , [ 1, 4, 0, 1 ] , [ 1, 6, 4, 1 ] , [ 3, 2, 0, 3 ] , [ 5, 4, 4, 5 ] | |||
8K0 | 24 | 1 | 12 | 2 | 0 | [ 0, 5, 3, 0 ] , [ 1, 0, 4, 1 ] , [ 1, 4, 4, 1 ] , [ 7, 4, 4, 7 ] | |||
8L0 | 24 | 1 | 12 | 4 | 0 | [ 0, 7, 1, 0 ] , [ 3, 6, 6, 7 ] , [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 2, 2, 3 ] | |||
8M0 | 32 | 2 | 16 | 4 | 2 | [ 0, 1, 7, 0 ] , [ 2, 3, 3, 5 ] , [ 7, 0, 0, 7 ] | |||
8N0 | 48 | 1 | 3 | 0 | 0 | [ 1, 0, 4, 1 ] , [ 1, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 4, 4, 7 ] | |||
8O0 | 48 | 1 | 6 | 0 | 0 | [ 1, 4, 0, 1 ] , [ 5, 6, 0, 5 ] , [ 7, 4, 0, 7 ] | |||
8P0 | 48 | 1 | 12 | 4 | 0 | [ 0, 7, 1, 0 ] , [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ] | |||
^ | Level 9 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/9Z) Matrix Generators |
9A0 | 9 | 1 | 9 | 5 | 0 | [ 0, 1, 8, 0 ] , [ 1, 7, 1, 8 ] , [ 2, 6, 6, 5 ] , [ 7, 0, 0, 4 ] , [ 7, 6, 6, 4 ] | |||
9B0 | Γ0(9) | 12 | 1 | 4 | 0 | 0 | [ 4, 0, 6, 7 ] , [ 7, 0, 6, 4 ] , [ 7, 0, 8, 4 ] , [ 8, 0, 0, 8 ] | ||
9C0 | 12 | 1 | 4 | 0 | 3 | [ 1, 3, 2, 7 ] , [ 4, 0, 6, 7 ] , [ 7, 0, 6, 4 ] , [ 8, 0, 0, 8 ] | |||
9D0 | 18 | 1 | 3 | 6 | 0 | [ 0, 1, 8, 0 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] , [ 7, 0, 0, 4 ] | |||
9E0 | 18 | 1 | 18 | 2 | 0 | [ 0, 1, 8, 0 ] , [ 4, 6, 3, 7 ] , [ 7, 0, 0, 4 ] , [ 8, 0, 0, 8 ] | |||
9F0 | 27 | 1 | 27 | 3 | 3 | [ 0, 1, 8, 0 ] , [ 0, 8, 1, 0 ] , [ 1, 3, 2, 7 ] , [ 4, 1, 1, 5 ] , [ 8, 0, 0, 8 ] | |||
9G0 | 27 | 1 | 27 | 7 | 0 | [ 0, 1, 8, 0 ] , [ 1, 7, 1, 8 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] | |||
9H0 | 36 | 1 | 6 | 0 | 0 | [ 4, 0, 0, 7 ] , [ 4, 3, 6, 7 ] , [ 8, 0, 0, 8 ] | |||
9I0 | Γ1(9) | 36 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 7, 0, 5, 4 ] , [ 8, 0, 0, 8 ] | ||
9J0 | 36 | 1 | 12 | 0 | 3 | [ 1, 0, 6, 1 ] , [ 1, 3, 2, 7 ] , [ 8, 0, 0, 8 ] | |||
^ | Level 10 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/10Z) Matrix Generators |
10A0 | 10 | 1 | 5 | 0 | 4 | [ 1, 4, 8, 3 ] , [ 1, 5, 5, 6 ] , [ 1, 8, 6, 9 ] , [ 3, 0, 8, 7 ] , [ 9, 0, 0, 9 ] | |||
10B0 | 12 | 1 | 6 | 4 | 0 | [ 6, 5, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 3, 1 ] | |||
10C0 | Γ0(10) | 18 | 1 | 18 | 2 | 0 | [ 1, 0, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 3, 1 ] | ||
10D0 | 20 | 1 | 10 | 4 | 2 | [ 1, 5, 5, 6 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] | |||
10E0 | 30 | 1 | 10 | 0 | 6 | [ 7, 6, 0, 3 ] , [ 8, 1, 7, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 2, 4, 1 ] | |||
10F0 | Γ1(10) | 36 | 1 | 18 | 0 | 0 | [ 5, 2, 2, 7 ] , [ 5, 2, 7, 7 ] , [ 9, 0, 0, 9 ] | ||
10G0 | 36 | 1 | 18 | 4 | 0 | [ 1, 4, 7, 9 ] , [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ] | |||
^ | Level 11 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/11Z) Matrix Generators |
11A0 | 11 | 2 | 11 | 3 | 2 | [ 8, 2, 6, 3 ] , [ 9, 4, 2, 1 ] , [ 10, 0, 0, 10 ] | |||
^ | Level 12 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/12Z) Matrix Generators |
12A0 | 12 | 1 | 4 | 6 | 0 | [ 1, 4, 4, 5 ] , [ 1, 9, 9, 10 ] , [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 4, 9 ] | |||
12B0 | 16 | 1 | 4 | 0 | 4 | [ 1, 6, 6, 1 ] , [ 3, 8, 10, 11 ] , [ 4, 3, 9, 7 ] , [ 7, 0, 6, 7 ] , [ 8, 1, 11, 3 ] , [ 9, 8, 4, 5 ] , [ 11, 0, 0, 11 ] | |||
12C0 | 18 | 1 | 3 | 6 | 0 | [ 1, 4, 4, 5 ] , [ 1, 6, 6, 1 ] , [ 4, 3, 9, 4 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 8, 9 ] | |||
12D0 | 18 | 1 | 9 | 4 | 0 | [ 1, 6, 6, 1 ] , [ 4, 3, 9, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 2, 9 ] , [ 10, 3, 9, 4 ] | |||
12E0 | Γ0(12) | 24 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 7, 0, 6, 7 ] , [ 9, 4, 8, 1 ] , [ 9, 8, 1, 5 ] , [ 9, 8, 4, 5 ] , [ 11, 4, 5, 3 ] , [ 11, 4, 8, 3 ] | ||
12F0 | 24 | 1 | 12 | 8 | 0 | [ 0, 1, 11, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 8, 1 ] , [ 7, 0, 0, 7 ] , [ 8, 1, 7, 4 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] | |||
12G0 | 36 | 1 | 9 | 4 | 0 | [ 1, 6, 6, 1 ] , [ 1, 10, 4, 5 ] , [ 4, 9, 3, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 2, 1 ] , [ 7, 0, 0, 7 ] | |||
12H0 | 36 | 1 | 9 | 8 | 0 | [ 0, 1, 11, 0 ] , [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 6, 6, 7 ] , [ 8, 11, 5, 4 ] , [ 11, 0, 0, 11 ] , [ 11, 4, 4, 7 ] | |||
12I0 | 48 | 1 | 12 | 0 | 0 | [ 1, 6, 0, 1 ] , [ 3, 4, 8, 7 ] , [ 5, 4, 8, 9 ] , [ 7, 6, 6, 7 ] , [ 9, 8, 4, 5 ] | |||
12J0 | Γ1(12) | 48 | 1 | 24 | 0 | 0 | [ 3, 4, 8, 7 ] , [ 5, 4, 2, 9 ] , [ 5, 4, 5, 9 ] , [ 9, 8, 1, 5 ] , [ 9, 8, 4, 5 ] | ||
^ | Level 13 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/13Z) Matrix Generators |
13A0 | Γ0(13) | 14 | 1 | 14 | 2 | 2 | [ 1, 3, 11, 8 ] , [ 7, 7, 4, 6 ] , [ 9, 2, 7, 6 ] , [ 12, 0, 0, 12 ] | ||
13B0 | 28 | 1 | 14 | 0 | 4 | [ 0, 3, 4, 2 ] , [ 4, 0, 11, 10 ] , [ 5, 7, 3, 7 ] | |||
13C0 | 42 | 1 | 14 | 6 | 0 | [ 0, 3, 4, 2 ] , [ 6, 6, 9, 7 ] , [ 7, 2, 7, 4 ] | |||
^ | Level 14 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/14Z) Matrix Generators |
14A0 | 14 | 2 | 7 | 4 | 2 | [ 1, 9, 4, 9 ] , [ 5, 8, 2, 9 ] , [ 7, 12, 4, 7 ] , [ 8, 7, 7, 1 ] , [ 11, 12, 0, 9 ] , [ 13, 0, 0, 13 ] | |||
14B0 | 16 | 1 | 8 | 0 | 4 | [ 1, 7, 7, 8 ] , [ 11, 8, 12, 5 ] , [ 13, 10, 2, 7 ] , [ 13, 12, 12, 9 ] | |||
14C0 | 48 | 1 | 16 | 0 | 6 | [ 0, 1, 13, 13 ] , [ 3, 10, 8, 13 ] , [ 11, 8, 12, 5 ] , [ 13, 0, 0, 13 ] | |||
^ | Level 15 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/15Z) Matrix Generators |
15A0 | 15 | 2 | 5 | 3 | 3 | [ 1, 3, 6, 4 ] , [ 1, 9, 8, 13 ] , [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 11, 0, 0, 11 ] , [ 11, 5, 5, 1 ] , [ 13, 0, 3, 7 ] | |||
15B0 | 18 | 1 | 6 | 6 | 0 | [ 6, 10, 5, 6 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 11, 5, 5, 1 ] , [ 14, 0, 0, 14 ] , [ 14, 1, 13, 1 ] | |||
15C0 | 36 | 1 | 18 | 8 | 0 | [ 2, 10, 7, 13 ] , [ 6, 10, 5, 6 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 14, 0, 0, 14 ] | |||
^ | Level 16 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/16Z) Matrix Generators |
16A0 | 16 | 2 | 8 | 2 | 4 | [ 1, 8, 8, 1 ] , [ 1, 9, 5, 14 ] , [ 1, 12, 4, 1 ] , [ 4, 5, 3, 4 ] , [ 9, 0, 8, 9 ] , [ 13, 0, 12, 5 ] , [ 14, 11, 7, 1 ] , [ 15, 8, 8, 15 ] | |||
16B0 | 24 | 1 | 3 | 8 | 0 | [ 1, 8, 8, 1 ] , [ 1, 10, 10, 5 ] , [ 2, 7, 13, 14 ] , [ 5, 4, 4, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 15, 0, 0, 15 ] , [ 15, 12, 12, 15 ] | |||
16C0 | Γ0(16) | 24 | 1 | 6 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 1, 12, 12, 1 ] , [ 5, 4, 12, 13 ] , [ 6, 1, 7, 12 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] , [ 13, 2, 6, 1 ] | ||
16D0 | 24 | 1 | 12 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 1, 12, 4, 1 ] , [ 2, 9, 7, 0 ] , [ 5, 4, 12, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] , [ 13, 2, 14, 1 ] | |||
16E0 | 24 | 1 | 12 | 2 | 0 | [ 1, 8, 8, 1 ] , [ 4, 3, 5, 4 ] , [ 9, 0, 0, 9 ] , [ 11, 6, 10, 7 ] , [ 13, 8, 8, 5 ] , [ 13, 12, 4, 5 ] , [ 15, 8, 8, 15 ] | |||
16F0 | 32 | 1 | 4 | 0 | 8 | [ 1, 8, 8, 1 ] , [ 7, 0, 8, 7 ] , [ 9, 0, 8, 9 ] , [ 9, 1, 5, 6 ] , [ 9, 4, 4, 9 ] , [ 13, 0, 12, 5 ] , [ 13, 8, 4, 5 ] , [ 15, 8, 8, 15 ] | |||
16G0 | 48 | 1 | 3 | 0 | 0 | [ 1, 4, 0, 1 ] , [ 1, 6, 0, 1 ] , [ 1, 8, 0, 1 ] , [ 3, 12, 8, 11 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 0, 9 ] , [ 13, 0, 8, 5 ] | |||
16H0 | 48 | 1 | 12 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 2, 1, 15, 0 ] , [ 9, 8, 8, 9 ] , [ 13, 4, 12, 5 ] , [ 13, 6, 10, 1 ] , [ 13, 12, 4, 5 ] , [ 15, 6, 10, 3 ] | |||
^ | Level 18 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/18Z) Matrix Generators |
18A0 | 18 | 2 | 9 | 8 | 0 | [ 1, 9, 9, 10 ] , [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 9, 10, 17, 9 ] , [ 11, 10, 1, 1 ] , [ 13, 6, 6, 7 ] | |||
18B0 | 24 | 1 | 4 | 0 | 6 | [ 1, 0, 6, 1 ] , [ 1, 9, 9, 10 ] , [ 1, 12, 2, 7 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] | |||
18C0 | 24 | 1 | 8 | 0 | 3 | [ 1, 0, 6, 1 ] , [ 1, 0, 10, 1 ] , [ 7, 15, 3, 4 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] | |||
18D0 | 36 | 1 | 3 | 12 | 0 | [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 7, 12, 12, 13 ] , [ 9, 10, 17, 9 ] , [ 10, 9, 9, 1 ] | |||
18E0 | Γ0(18) | 36 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 9, 1 ] , [ 1, 0, 12, 1 ] , [ 7, 0, 14, 13 ] , [ 13, 0, 0, 7 ] , [ 17, 0, 0, 17 ] | ||
^ | Level 20 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/20Z) Matrix Generators |
20A0 | 36 | 1 | 18 | 4 | 0 | [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 5, 12, 17, 17 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 10, 11 ] , [ 11, 14, 17, 9 ] | |||
^ | Level 21 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/21Z) Matrix Generators |
21A0 | 21 | 2 | 7 | 9 | 0 | [ 1, 7, 7, 8 ] , [ 1, 18, 3, 13 ] , [ 6, 17, 4, 15 ] , [ 7, 3, 9, 7 ] , [ 7, 15, 6, 13 ] , [ 8, 0, 0, 8 ] , [ 10, 15, 18, 4 ] , [ 13, 0, 0, 13 ] , [ 15, 7, 14, 15 ] | |||
^ | Level 24 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/24Z) Matrix Generators |
24A0 | 36 | 1 | 3 | 12 | 0 | [ 1, 0, 12, 1 ] , [ 1, 8, 20, 17 ] , [ 1, 16, 4, 17 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 6, 13 ] , [ 13, 12, 18, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 3, 13 ] | |||
24B0 | 48 | 1 | 12 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 8, 0, 1 ] , [ 7, 12, 6, 7 ] , [ 11, 0, 21, 11 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 12, 13 ] , [ 19, 12, 15, 7 ] , [ 23, 0, 0, 23 ] | |||
^ | Level 25 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/25Z) Matrix Generators |
25A0 | Γ0(25) | 30 | 1 | 30 | 2 | 0 | [ 6, 10, 20, 21 ] , [ 8, 21, 6, 19 ] , [ 9, 11, 18, 11 ] , [ 11, 0, 10, 16 ] , [ 24, 0, 0, 24 ] | ||
25B0 | 60 | 1 | 6 | 0 | 0 | [ 6, 0, 5, 21 ] , [ 6, 15, 15, 21 ] , [ 7, 23, 18, 20 ] , [ 16, 0, 15, 11 ] , [ 19, 0, 20, 4 ] | |||
^ | Level 26 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/26Z) Matrix Generators |
26A0 | 28 | 1 | 14 | 4 | 4 | [ 5, 20, 16, 7 ] , [ 11, 14, 3, 11 ] , [ 13, 16, 4, 15 ] , [ 14, 13, 13, 1 ] , [ 17, 0, 24, 23 ] | |||
^ | Level 27 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/27Z) Matrix Generators |
27A0 | 36 | 1 | 12 | 0 | 0 | [ 1, 0, 18, 1 ] , [ 10, 0, 0, 19 ] , [ 10, 0, 24, 19 ] , [ 13, 9, 1, 7 ] , [ 16, 18, 25, 13 ] , [ 26, 0, 0, 26 ] | |||
^ | Level 28 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/28Z) Matrix Generators |
28A0 | 32 | 1 | 8 | 0 | 8 | [ 1, 14, 14, 1 ] , [ 13, 14, 0, 13 ] , [ 13, 20, 8, 21 ] , [ 15, 14, 0, 15 ] , [ 17, 24, 8, 13 ] , [ 22, 21, 21, 1 ] , [ 25, 8, 12, 5 ] | |||
^ | Level 30 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/30Z) Matrix Generators |
30A0 | 36 | 1 | 6 | 12 | 0 | [ 1, 10, 10, 11 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 0, 11 ] , [ 16, 15, 15, 1 ] , [ 21, 10, 20, 21 ] , [ 27, 25, 2, 3 ] , [ 29, 0, 0, 29 ] | |||
^ | Level 32 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/32Z) Matrix Generators |
32A0 | 48 | 1 | 6 | 0 | 0 | [ 1, 16, 16, 1 ] , [ 1, 28, 28, 17 ] , [ 5, 20, 12, 29 ] , [ 9, 8, 24, 25 ] , [ 9, 24, 8, 25 ] , [ 11, 26, 6, 23 ] , [ 13, 4, 12, 21 ] , [ 17, 10, 6, 13 ] , [ 17, 16, 16, 17 ] , [ 19, 26, 22, 15 ] , [ 23, 10, 30, 27 ] , [ 26, 29, 27, 8 ] | |||
^ | Level 36 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/36Z) Matrix Generators |
36A0 | 48 | 1 | 4 | 0 | 12 | [ 1, 0, 24, 1 ] , [ 1, 18, 18, 1 ] , [ 10, 27, 27, 1 ] , [ 19, 18, 0, 19 ] , [ 25, 0, 24, 13 ] , [ 25, 24, 16, 1 ] , [ 35, 0, 0, 35 ] | |||
^ | Level 48 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/48Z) Matrix Generators |
48A0 | 72 | 1 | 3 | 24 | 0 | [ 1, 0, 24, 1 ] , [ 3, 10, 47, 45 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 20, 14, 17 ] , [ 33, 32, 16, 33 ] , [ 37, 0, 36, 13 ] , [ 41, 24, 36, 41 ] |