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Level Weight Analytic conductor \(Nk^2\)
Bad \(p\) Char. Primitive character Character order

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 1 1 2 2 3 3 4 4 5 5 6 6 8 7 8 8 9 10 12 10 12 12
2 0 1 1 2 3 3 5 5 7 7 10 9 13 12 16 15 20 17 24 22 28 25 33 28
3 0 0 2 2 4 4 7 7 10 10 15 13 20 18 24 23 32 26 39 34 44 40 55 44
4 1 2 2 3 5 5 9 9 13 13 20 17 27 24 32 31 44 35 54 46 60 55 77 60
5 0 0 2 3 6 6 11 11 16 16 25 21 34 30 40 39 56 44 69 58 76 70 99 76
6 1 2 3 4 7 7 13 13 19 19 30 25 41 36 48 47 68 53 84 70 92 85 121 92
7 0 0 3 4 8 8 15 15 22 22 35 29 48 42 56 55 80 62 99 82 108 100 143 108
8 1 3 3 5 9 9 17 17 25 25 40 33 55 48 64 63 92 71 114 94 124 115 165 124
9 0 0 4 5 10 10 19 19 28 28 45 37 62 54 72 71 104 80 129 106 140 130 187 140
10 1 3 4 6 11 11 21 21 31 31 50 41 69 60 80 79 116 89 144 118 156 145 209 156
11 0 0 4 6 12 12 23 23 34 34 55 45 76 66 88 87 128 98 159 130 172 160 231 172
12 2 4 5 7 13 13 25 25 37 37 60 49 83 72 96 95 140 107 174 142 188 175 253 188
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 1 1 2 0 3 1 2 0 5 0 6 0 2 2 8 0 9 2 4 0 12 2
2 0 1 1 0 3 0 5 2 5 0 10 4 13 1 9 7 20 2 24 11 17 4 33 9
3 0 0 2 2 4 0 7 3 6 2 15 3 20 4 12 11 32 6 39 14 26 10 55 16
4 1 0 0 0 3 1 7 5 10 3 18 9 25 6 22 16 42 7 52 25 42 15 75 21
5 0 0 2 3 6 2 11 5 12 4 25 5 34 8 24 20 56 8 69 26 50 20 99 30
6 1 0 1 1 5 1 11 7 14 5 28 12 39 10 32 25 66 13 82 37 64 25 119 35
7 0 0 3 4 8 2 15 7 16 6 35 8 48 12 34 29 80 14 99 38 72 30 143 44
8 1 1 1 0 7 1 15 10 20 5 38 18 53 12 44 34 90 16 112 53 88 33 163 47
9 0 0 4 5 10 2 19 9 20 8 45 11 62 16 44 38 104 20 129 50 94 40 187 58
10 1 1 2 1 9 1 19 12 24 7 48 21 67 16 54 43 114 22 142 65 110 43 207 61
11 0 0 4 6 12 4 23 11 26 10 55 13 76 20 56 47 128 22 159 62 118 50 231 72
12 2 0 1 1 9 3 21 15 29 11 56 26 79 22 68 52 136 27 170 79 136 55 249 73
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 2 0 2 2 4 0 5 0 6 6 5 0 8 0 8 8 10 0 10
2 0 0 0 2 0 3 0 3 2 7 0 5 0 11 7 8 0 15 0 11 11 21 0 19
3 0 0 0 0 0 4 0 4 4 8 0 10 0 14 12 12 0 20 0 20 18 30 0 28
4 0 2 2 3 2 4 2 4 3 10 2 8 2 18 10 15 2 28 2 21 18 40 2 39
5 0 0 0 0 0 4 0 6 4 12 0 16 0 22 16 19 0 36 0 32 26 50 0 46
6 0 2 2 3 2 6 2 6 5 14 2 13 2 26 16 22 2 40 2 33 28 60 2 57
7 0 0 0 0 0 6 0 8 6 16 0 21 0 30 22 26 0 48 0 44 36 70 0 64
8 0 2 2 5 2 8 2 7 5 20 2 15 2 36 20 29 2 55 2 41 36 82 2 77
9 0 0 0 0 0 8 0 10 8 20 0 26 0 38 28 33 0 60 0 56 46 90 0 82
10 0 2 2 5 2 10 2 9 7 24 2 20 2 44 26 36 2 67 2 53 46 102 2 95
11 0 0 0 0 0 8 0 12 8 24 0 32 0 46 32 40 0 76 0 68 54 110 0 100
12 0 4 4 6 4 10 4 10 8 26 4 23 4 50 28 43 4 80 4 63 52 120 4 115
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 1 0
2 0 0 0 0 0 0 0 0 0 0 1 0 2 1 1 2 5 2 7 3 5 6 12 5
3 0 0 0 0 0 0 1 1 2 2 5 3 8 6 8 9 16 10 21 14 20 20 33 20
4 0 0 0 0 1 1 3 3 5 5 10 7 15 12 16 17 28 19 36 26 36 35 55 36
5 0 0 0 1 2 2 5 5 8 8 15 11 22 18 24 25 40 28 51 38 52 50 77 52
6 0 0 1 1 3 3 7 7 11 11 20 15 29 24 32 33 52 37 66 50 68 65 99 68
7 0 0 1 2 4 4 9 9 14 14 25 19 36 30 40 41 64 46 81 62 84 80 121 84
8 0 1 1 2 5 5 11 11 17 17 30 23 43 36 48 49 76 55 96 74 100 95 143 100
9 0 0 2 3 6 6 13 13 20 20 35 27 50 42 56 57 88 64 111 86 116 110 165 116
10 0 1 2 3 7 7 15 15 23 23 40 31 57 48 64 65 100 73 126 98 132 125 187 132
11 0 0 2 4 8 8 17 17 26 26 45 35 64 54 72 73 112 82 141 110 148 140 209 148
12 1 2 3 4 9 9 19 19 29 29 50 39 71 60 80 81 124 91 156 122 164 155 231 164
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 1 0
2 0 0 0 0 0 0 0 0 0 0 1 0 2 1 1 2 5 2 7 3 5 4 12 5
3 0 0 0 0 0 0 1 1 2 2 5 3 8 4 8 7 16 6 21 10 18 10 33 12
4 0 0 0 0 1 1 3 3 5 3 10 5 15 6 14 11 28 7 36 17 30 15 55 17
5 0 0 0 1 2 2 5 3 8 4 15 5 22 8 20 16 40 8 51 22 42 20 77 26
6 0 0 1 1 3 1 7 5 9 5 20 8 29 10 24 20 52 13 66 29 52 25 99 31
7 0 0 1 2 4 2 9 5 12 6 25 8 36 12 30 25 64 14 81 34 64 30 121 40
8 0 1 1 0 5 1 11 8 15 5 30 14 43 12 36 29 76 16 96 45 76 33 143 43
9 0 0 2 3 6 2 13 7 16 8 35 11 50 16 40 34 88 20 111 46 86 40 165 54
10 0 1 2 1 7 1 15 10 19 7 40 17 57 16 46 38 100 22 126 57 98 43 187 57
11 0 0 2 4 8 4 17 9 22 10 45 13 64 20 52 43 112 22 141 58 110 50 209 68
12 1 0 1 1 7 3 17 13 24 11 48 22 69 22 60 47 122 27 154 71 124 55 229 69
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 2 0 2 0 4 0 4 2 10 0 8
4 0 0 0 0 0 0 0 0 0 2 0 2 0 6 2 6 0 12 0 9 6 20 0 19
5 0 0 0 0 0 0 0 2 0 4 0 6 0 10 4 9 0 20 0 16 10 30 0 26
6 0 0 0 0 0 2 0 2 2 6 0 7 0 14 8 13 0 24 0 21 16 40 0 37
7 0 0 0 0 0 2 0 4 2 8 0 11 0 18 10 16 0 32 0 28 20 50 0 44
8 0 0 0 2 0 4 0 3 2 12 0 9 0 24 12 20 0 39 0 29 24 62 0 57
9 0 0 0 0 0 4 0 6 4 12 0 16 0 26 16 23 0 44 0 40 30 70 0 62
10 0 0 0 2 0 6 0 5 4 16 0 14 0 32 18 27 0 51 0 41 34 82 0 75
11 0 0 0 0 0 4 0 8 4 16 0 22 0 34 20 30 0 60 0 52 38 90 0 80
12 0 2 2 3 2 6 2 6 5 18 2 17 2 38 20 34 2 64 2 51 40 100 2 95
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 1 1 2 2 3 3 4 4 5 5 6 6 8 7 8 8 9 10 12 10 11 12
2 0 1 1 2 3 3 5 5 7 7 9 9 11 11 15 13 15 15 17 19 23 19 21 23
3 0 0 2 2 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
4 1 2 2 3 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
5 0 0 2 2 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
6 1 2 2 3 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
7 0 0 2 2 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
8 1 2 2 3 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
9 0 0 2 2 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
10 1 2 2 3 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
11 0 0 2 2 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
12 1 2 2 3 4 4 6 6 8 8 10 10 12 12 16 14 16 16 18 20 24 20 22 24
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 1 1 2 0 3 1 2 0 5 0 6 0 2 2 8 0 9 2 4 0 11 2
2 0 1 1 0 3 0 5 2 5 0 9 4 11 0 8 5 15 0 17 8 12 0 21 4
3 0 0 2 2 4 0 6 2 4 0 10 0 12 0 4 4 16 0 18 4 8 0 22 4
4 1 0 0 0 2 0 4 2 5 0 8 4 10 0 8 5 14 0 16 8 12 0 20 4
5 0 0 2 2 4 0 6 2 4 0 10 0 12 0 4 4 16 0 18 4 8 0 22 4
6 1 0 0 0 2 0 4 2 5 0 8 4 10 0 8 5 14 0 16 8 12 0 20 4
7 0 0 2 2 4 0 6 2 4 0 10 0 12 0 4 4 16 0 18 4 8 0 22 4
8 1 0 0 0 2 0 4 2 5 0 8 4 10 0 8 5 14 0 16 8 12 0 20 4
9 0 0 2 2 4 0 6 2 4 0 10 0 12 0 4 4 16 0 18 4 8 0 22 4
10 1 0 0 0 2 0 4 2 5 0 8 4 10 0 8 5 14 0 16 8 12 0 20 4
11 0 0 2 2 4 0 6 2 4 0 10 0 12 0 4 4 16 0 18 4 8 0 22 4
12 1 0 0 0 2 0 4 2 5 0 8 4 10 0 8 5 14 0 16 8 12 0 20 4
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 2 0 2 2 4 0 5 0 6 6 5 0 8 0 8 8 10 0 10
2 0 0 0 2 0 3 0 3 2 7 0 5 0 11 7 8 0 15 0 11 11 19 0 19
3 0 0 0 0 0 4 0 4 4 8 0 10 0 12 12 10 0 16 0 16 16 20 0 20
4 0 2 2 3 2 4 2 4 3 8 2 6 2 12 8 9 2 16 2 12 12 20 2 20
5 0 0 0 0 0 4 0 4 4 8 0 10 0 12 12 10 0 16 0 16 16 20 0 20
6 0 2 2 3 2 4 2 4 3 8 2 6 2 12 8 9 2 16 2 12 12 20 2 20
7 0 0 0 0 0 4 0 4 4 8 0 10 0 12 12 10 0 16 0 16 16 20 0 20
8 0 2 2 3 2 4 2 4 3 8 2 6 2 12 8 9 2 16 2 12 12 20 2 20
9 0 0 0 0 0 4 0 4 4 8 0 10 0 12 12 10 0 16 0 16 16 20 0 20
10 0 2 2 3 2 4 2 4 3 8 2 6 2 12 8 9 2 16 2 12 12 20 2 20
11 0 0 0 0 0 4 0 4 4 8 0 10 0 12 12 10 0 16 0 16 16 20 0 20
12 0 2 2 3 2 4 2 4 3 8 2 6 2 12 8 9 2 16 2 12 12 20 2 20