Learn more about

Refine search

Use these links to change the kind of modular form space whose dimension is displayed in the table.

All modular forms New modular forms Old modular forms
All cusp forms New cusp forms Old cusp forms
All Eisenstein series New Eisenstein series Old Eisenstein series

The dimensions shown are for spaces of modular forms in each weight and level that satisfy the specified conditions.

Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 2 1 3 1 3 3 3 2 5 1 4 4 5 2 7 2 6 4 5 3 8
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 2 2 3 3 5 3 5 5 7 4 9 5 8 8 9 6 13 6 12 10 11 7 16
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 1 2 3 4 3 7 5 7 7 9 6 13 7 12 12 13 8 19 10 18 16 17 11 24
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 3 3 5 5 9 5 9 9 13 8 17 9 16 16 17 12 25 12 24 20 23 15 32
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 1 3 4 6 5 11 7 11 11 15 10 21 11 20 20 21 14 31 16 30 26 29 19 40
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 2 4 5 7 7 13 9 13 13 19 12 25 15 24 24 25 18 37 20 36 32 35 23 48
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 1 0 1 0 1 0 2 0 1 1 1 1 2 0 2 1 1 0 3 1
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 0 0 0 1 1 1 1 2 1 2 1 3 2 2 2 4 1 4 1 4 3 5 1
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 1 0 1 1 1 1 3 1 2 3 4 0 5 2 4 3 6 3 8 1 4 5 9 3
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 1 1 0 3 1 3 2 4 1 6 2 7 4 4 4 10 2 10 3 8 5 13 3
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 1 1 2 1 3 1 5 2 4 3 8 1 9 4 6 5 12 4 14 3 8 7 17 5
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 2 0 1 1 3 3 5 3 5 5 8 2 11 6 8 6 14 5 16 3 12 11 19 5
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 2 0 3 0 3 2 3 0 5 0 3 3 4 0 7 0 5 3 5 0 7
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 2 3 2 4 2 4 3 6 2 8 2 6 6 7 2 12 2 11 6 8 2 15
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 2 2 3 2 6 2 6 5 6 2 13 2 10 8 10 2 16 2 17 12 12 2 21
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 2 2 5 2 8 2 7 5 12 2 15 2 12 12 13 2 23 2 21 12 18 2 29
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 2 2 5 2 10 2 9 7 12 2 20 2 16 14 16 2 27 2 27 18 22 2 35
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 4 4 6 4 10 4 10 8 14 4 23 4 18 16 19 4 32 4 33 20 24 4 43
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 2 2 1
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 1 1 1 1 1 3 2 3 3 4 4 3 4 5 4 6 6 7 5 8
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 1 1 1 3 3 3 3 5 4 7 5 8 8 7 6 11 8 12 12 13 9 16
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 1 1 2 3 5 3 5 5 9 6 11 7 12 12 11 10 17 10 18 16 19 13 24
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 1 2 3 3 7 5 7 7 11 8 15 9 16 16 15 12 23 14 24 22 25 17 32
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 1 2 3 4 5 9 7 9 9 15 10 19 13 20 20 19 16 29 18 30 28 31 21 40
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 2 1
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 1 1 1 1 1 1 2 1 3 2 2 1 4 1 4 1 4 3 5 1
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 1 1 1 1 3 1 1 3 4 0 5 2 4 2 6 3 8 1 4 5 9 3
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 1 1 0 3 1 3 2 3 1 6 2 7 4 4 3 10 2 10 3 8 5 13 3
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 1 2 1 3 1 5 2 3 3 8 1 9 4 6 4 12 4 14 3 8 7 17 5
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 1 0 1 1 3 3 5 3 4 5 8 2 11 6 8 5 14 5 16 3 12 11 19 5
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 0 4 0 5 2 4 0 7
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 2 0 2 2 2 0 7 0 6 4 5 0 8 0 11 8 8 0 13
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 2 0 4 0 3 2 8 0 9 0 8 8 8 0 15 0 15 8 14 0 21
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 2 0 6 0 5 4 8 0 14 0 12 10 11 0 19 0 21 14 18 0 27
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 2 2 3 2 6 2 6 5 10 2 17 2 14 12 14 2 24 2 27 16 20 2 35
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 2 1 3 1 3 3 3 1 5 1 3 3 5 1 7 1 5 3 3 1 7
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 2 2 3 2 4 2 4 4 4 2 6 2 4 4 6 2 8 2 6 4 4 2 8
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 1 2 2 3 2 4 2 4 4 4 2 6 2 4 4 6 2 8 2 6 4 4 2 8
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 2 2 3 2 4 2 4 4 4 2 6 2 4 4 6 2 8 2 6 4 4 2 8
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 1 2 2 3 2 4 2 4 4 4 2 6 2 4 4 6 2 8 2 6 4 4 2 8
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 1 2 2 3 2 4 2 4 4 4 2 6 2 4 4 6 2 8 2 6 4 4 2 8
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
Level
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weight
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 2 0 3 0 3 2 3 0 5 0 3 3 4 0 7 0 5 3 3 0 7
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 8 2 6 4 4 2 8
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 8 2 6 4 4 2 8
7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 8 2 6 4 4 2 8
9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10 0 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 8 2 6 4 4 2 8
11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5 2 8 2 6 4 4 2 8