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The database currently contains 198,886 Bianchi modular forms of weight 2 over 11 imaginary quadratic fields, and 370,670 spaces of cusp forms over 12 imaginary quadratic fields, including all with class number one.

Distribution of Bianchi modular forms by base field and level norm

level norm
1-100 101-1000 1001-10000 10001-50000 50001-100000 100001-150000 Total
base field
\(\Q(\sqrt{-3}) \) 3 127 2080 11072 14445 14616 42343
0.01% 0.30% 4.91% 26.15% 34.11% 34.52% 21.31%
\(\Q(\sqrt{-1}) \) 5 188 2967 15982 20888 40030
0.01% 0.47% 7.41% 39.93% 52.18% 20.15%
\(\Q(\sqrt{-7}) \) 16 301 5606 29901 35824
0.04% 0.84% 15.65% 83.47% 18.03%
\(\Q(\sqrt{-2}) \) 10 345 5884 30604 36843
0.03% 0.94% 15.97% 83.07% 18.55%
\(\Q(\sqrt{-11}) \) 12 314 4879 25336 30541
0.04% 1.03% 15.98% 82.96% 15.37%
\(\Q(\sqrt{-19}) \) 11 200 2386 1386 3983
0.28% 5.02% 59.90% 34.80% 2.00%
\(\Q(\sqrt{-23}) \) 41 889 1384 2314
1.77% 38.42% 59.81% 1.16%
\(\Q(\sqrt{-31}) \) 52 759 4352 5163
1.01% 14.70% 84.29% 2.60%
\(\Q(\sqrt{-43}) \) 1 65 653 345 1064
0.09% 6.11% 61.37% 32.42% 0.54%
\(\Q(\sqrt{-67}) \) 1 31 419 451
0.22% 6.87% 92.90% 0.23%
\(\Q(\sqrt{-163}) \) 26 85 111
23.42% 76.58% 0.06%
Total 152 3245 30695 114626 35333 14616 198667
0.08% 1.63% 15.45% 57.70% 17.79% 7.36%

Distribution of computed $\operatorname{GL}_2$ levels by base field and level norm

The set of weights computed for each level varies.

level norm
1-100 101-1000 1001-10000 10001-50000 50001-100000 100001-150000 Total
base field
\(\Q(\sqrt{-3}) \) 3 161 2368 11389 14356 14526 42803
0.01% 0.38% 5.53% 26.61% 33.54% 33.94% 22.68%
\(\Q(\sqrt{-1}) \) 5 253 3425 16061 20206 39950
0.01% 0.63% 8.57% 40.20% 50.58% 21.16%
\(\Q(\sqrt{-7}) \) 24 477 6053 27474 34028
0.07% 1.40% 17.79% 80.74% 18.03%
\(\Q(\sqrt{-2}) \) 13 417 5279 23925 29634
0.04% 1.41% 17.81% 80.73% 15.70%
\(\Q(\sqrt{-11}) \) 20 368 4434 20228 25050
0.08% 1.47% 17.70% 80.75% 13.27%
\(\Q(\sqrt{-19}) \) 18 252 2683 1590 4543
0.40% 5.55% 59.06% 35.00% 2.41%
\(\Q(\sqrt{-23}) \) 198 2130 1212 3540
5.59% 60.17% 34.24% 1.88%
\(\Q(\sqrt{-31}) \) 164 1796 4108 6068
2.70% 29.60% 67.70% 3.21%
\(\Q(\sqrt{-43}) \) 6 100 1222 713 2041
0.29% 4.90% 59.87% 34.93% 1.08%
\(\Q(\sqrt{-67}) \) 6 69 872 947
0.63% 7.29% 92.08% 0.50%
\(\Q(\sqrt{-163}) \) 2 34 122 158
1.27% 21.52% 77.22% 0.08%

Distribution of computed $\operatorname{SL}_2$ levels by base field and level norm

The set of weights computed for each level varies.

level norm
1-100 101-200 201-400 401-800 801-1600 1601-3200 3201-6400 Total
base field
\(\Q(\sqrt{-3}) \) 5 1 1 7
71.43% 14.29% 14.29% 0.15%
\(\Q(\sqrt{-1}) \) 63 47 88 196 131 525
12.00% 8.95% 16.76% 37.33% 24.95% 11.34%
\(\Q(\sqrt{-7}) \) 105 74 142 297 500 142 1260
8.33% 5.87% 11.27% 23.57% 39.68% 11.27% 27.22%
\(\Q(\sqrt{-2}) \) 107 71 109 218 175 680
15.74% 10.44% 16.03% 32.06% 25.74% 14.69%
\(\Q(\sqrt{-11}) \) 97 91 132 222 402 202 1146
8.46% 7.94% 11.52% 19.37% 35.08% 17.63% 24.76%
\(\Q(\sqrt{-19}) \) 74 71 136 99 114 494
14.98% 14.37% 27.53% 20.04% 23.08% 10.67%
\(\Q(\sqrt{-5}) \) 3 3
100.00% 0.06%
\(\Q(\sqrt{-43}) \) 47 51 91 161 1 351
13.39% 14.53% 25.93% 45.87% 0.28% 7.58%
\(\Q(\sqrt{-67}) \) 39 40 55 1 135
28.89% 29.63% 40.74% 0.74% 2.92%
\(\Q(\sqrt{-163}) \) 25 3 28
89.29% 10.71% 0.60%