The database currently contains 35,416 Maass forms of weight 0 on $\Gamma_0(N)$ for $N$ in the range from 1 to 105.
Distribution of levels and spectral parameters
spectral parameter | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0-1 | 1-2 | 2-3 | 3-4 | 4-6 | 6-10 | 10-20 | 20-32 | Total | ||
level
|
1 | 1 | 9 | 29 | 39 | |||||
2.56% | 23.08% | 74.36% | 0.12% | |||||||
2-13 | 1 | 2 | 11 | 16 | 55 | 192 | 965 | 511 | 1753 | |
0.06% | 0.11% | 0.63% | 0.91% | 3.14% | 10.95% | 55.05% | 29.15% | 5.27% | ||
14-20 | 10 | 15 | 24 | 73 | 242 | 1153 | 113 | 1630 | ||
0.61% | 0.92% | 1.47% | 4.48% | 14.85% | 70.74% | 6.93% | 4.90% | |||
21-30 | 2 | 17 | 36 | 51 | 145 | 469 | 1842 | 2562 | ||
0.08% | 0.66% | 1.41% | 1.99% | 5.66% | 18.31% | 71.90% | 7.70% | |||
31-105 | 121 | 515 | 825 | 1117 | 2874 | 7592 | 14225 | 27269 | ||
0.44% | 1.89% | 3.03% | 4.10% | 10.54% | 27.84% | 52.17% | 82.00% | |||
Total | 124 | 544 | 887 | 1208 | 3147 | 8496 | 18194 | 653 | 33253 | |
0.37% | 1.64% | 2.67% | 3.63% | 9.46% | 25.55% | 54.71% | 1.96% |
Distribution of symmetries and levels
level | |||||||
---|---|---|---|---|---|---|---|
1 | 2-13 | 14-20 | 21-30 | 31-105 | Total | ||
symmetry
|
even | 1110 | 849 | 803 | 1279 | 14312 | 18353 |
50.41% | 48.43% | 49.26% | 49.92% | 52.48% | 51.82% | ||
odd | 1092 | 904 | 827 | 1283 | 12957 | 17063 | |
49.59% | 51.57% | 50.74% | 50.08% | 47.52% | 48.18% | ||
Total | 2202 | 1753 | 1630 | 2562 | 27269 | 35416 | |
6.22% | 4.95% | 4.60% | 7.23% | 77.00% |
Distribution of symmetries and spectral parameters
spectral parameter | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0-1 | 1-2 | 2-3 | 3-4 | 4-6 | 6-10 | 10-20 | 20-32 | Total | ||
symmetry
|
even | 49 | 257 | 449 | 654 | 1701 | 4494 | 9321 | 332 | 17257 |
39.52% | 47.24% | 50.62% | 54.14% | 54.05% | 52.90% | 51.23% | 50.84% | 51.90% | ||
odd | 75 | 287 | 438 | 554 | 1446 | 4002 | 8873 | 321 | 15996 | |
60.48% | 52.76% | 49.38% | 45.86% | 45.95% | 47.10% | 48.77% | 49.16% | 48.10% | ||
Total | 124 | 544 | 887 | 1208 | 3147 | 8496 | 18194 | 653 | 33253 | |
0.37% | 1.64% | 2.67% | 3.63% | 9.46% | 25.55% | 54.71% | 1.96% |