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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%