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

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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