Bianchi modular forms: statistics

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%