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% |