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The database currently contains 185,800 Bianchi modular forms of weight 2 over 5 imaginary quadratic fields. It also contains 332,694 spaces of cusp forms over 10 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% 22.79%
\(\Q(\sqrt{-1}) \) 5 201 3173 15982 20888 40249
0.01% 0.50% 7.88% 39.71% 51.90% 21.66%
\(\Q(\sqrt{-7}) \) 16 301 5606 29901 35824
0.04% 0.84% 15.65% 83.47% 19.28%
\(\Q(\sqrt{-2}) \) 10 345 5884 30604 36843
0.03% 0.94% 15.97% 83.07% 19.83%
\(\Q(\sqrt{-11}) \) 12 314 4879 25336 30541
0.04% 1.03% 15.98% 82.96% 16.44%
Total 46 1288 21622 112895 35333 14616 185800
0.02% 0.69% 11.64% 60.76% 19.02% 7.87%

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% 24.96%
\(\Q(\sqrt{-1}) \) 5 253 3425 16061 20206 39950
0.01% 0.63% 8.57% 40.20% 50.58% 23.30%
\(\Q(\sqrt{-7}) \) 24 477 6053 27474 34028
0.07% 1.40% 17.79% 80.74% 19.85%
\(\Q(\sqrt{-2}) \) 13 417 5279 23925 29634
0.04% 1.41% 17.81% 80.73% 17.28%
\(\Q(\sqrt{-11}) \) 20 368 4434 20228 25050
0.08% 1.47% 17.70% 80.75% 14.61%

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%

Distribution of newform dimensions and level norms

level norm
1-100 101-1000 1001-10000 10001-50000 50001-100000 100001-150000 Total
dimension
1 46 1275 21416 112895 35333 14616 185581
100.00% 98.99% 99.05% 100.00% 100.00% 100.00% 99.88%
2 13 206 219
1.01% 0.95% 0.12%
Total 46 1288 21622 112895 35333 14616 185800
0.02% 0.69% 11.64% 60.76% 19.02% 7.87%

Distribution of newform dimensions and base fields

base field
\(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-11}) \) Total
dimension
1 42343 40030 35824 36843 30541 185581
100.00% 99.46% 100.00% 100.00% 100.00% 99.88%
2 219 219
0.54% 0.12%
Total 42343 40249 35824 36843 30541 185800
22.79% 21.66% 19.28% 19.83% 16.44%