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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%