The database currently contains 14,995 Maass forms of weight 0 on $\Gamma_0(N)$ for $N$ in the range from 1 to 997.
Distribution of levels and spectral parameters
spectral parameter | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0-1 | 1-2 | 2-3 | 3-4 | 4-6 | 6-10 | 10-20 | 20-32 | 32-50 | Total | ||
level
|
1 | 1 | 9 | 24 | 35 | 69 | |||||
1.45% | 13.04% | 34.78% | 50.72% | 0.46% | |||||||
2-13 | 1 | 3 | 13 | 20 | 66 | 229 | 1083 | 2276 | 3691 | ||
0.03% | 0.08% | 0.35% | 0.54% | 1.79% | 6.20% | 29.34% | 61.66% | 24.61% | |||
14-20 | 12 | 18 | 23 | 83 | 269 | 1290 | 1695 | ||||
0.71% | 1.06% | 1.36% | 4.90% | 15.87% | 76.11% | 11.30% | |||||
21-30 | 3 | 21 | 46 | 55 | 137 | 397 | 659 | ||||
0.46% | 3.19% | 6.98% | 8.35% | 20.79% | 60.24% | 4.39% | |||||
31-100 | 122 | 536 | 719 | 1004 | 227 | 4 | 2612 | ||||
4.67% | 20.52% | 27.53% | 38.44% | 8.69% | 0.15% | 17.42% | |||||
101-997 | 5181 | 1088 | 6269 | ||||||||
82.64% | 17.36% | 41.81% | |||||||||
Total | 5307 | 1660 | 796 | 1102 | 513 | 900 | 2382 | 2300 | 35 | 14995 | |
35.39% | 11.07% | 5.31% | 7.35% | 3.42% | 6.00% | 15.89% | 15.34% | 0.23% |
Distribution of symmetries and levels
level | ||||||||
---|---|---|---|---|---|---|---|---|
1 | 2-13 | 14-20 | 21-30 | 31-100 | 101-997 | Total | ||
symmetry
|
odd | 21 | 1907 | 861 | 334 | 1326 | 3219 | 7668 |
30.43% | 51.67% | 50.80% | 50.68% | 50.77% | 51.35% | 51.14% | ||
even | 48 | 1784 | 834 | 325 | 1286 | 3050 | 7327 | |
69.57% | 48.33% | 49.20% | 49.32% | 49.23% | 48.65% | 48.86% | ||
Total | 69 | 3691 | 1695 | 659 | 2612 | 6269 | 14995 | |
0.46% | 24.61% | 11.30% | 4.39% | 17.42% | 41.81% |
Distribution of symmetries and spectral parameters
spectral parameter | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0-1 | 1-2 | 2-3 | 3-4 | 4-6 | 6-10 | 10-20 | 20-32 | 32-50 | Total | ||
symmetry
|
odd | 2746 | 844 | 410 | 556 | 252 | 461 | 1225 | 1174 | 7668 | |
51.74% | 50.84% | 51.51% | 50.45% | 49.12% | 51.22% | 51.43% | 51.04% | 51.14% | |||
even | 2561 | 816 | 386 | 546 | 261 | 439 | 1157 | 1126 | 35 | 7327 | |
48.26% | 49.16% | 48.49% | 49.55% | 50.88% | 48.78% | 48.57% | 48.96% | 100.00% | 48.86% | ||
Total | 5307 | 1660 | 796 | 1102 | 513 | 900 | 2382 | 2300 | 35 | 14995 | |
35.39% | 11.07% | 5.31% | 7.35% | 3.42% | 6.00% | 15.89% | 15.34% | 0.23% |