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Prime-Level Census: Singular 3-adic Hecke Nodes

Scan primes N <= 1000.

level	dim S2	qdim	category	alg_dim	idemp_mod3	lift_z3	T2	minpoly	T2 rank	r3	r9	r27
11	1	0	smooth	0	false	false	x	0	0	0	0	0
13	0	0	smooth	0	false	false	x	0	0	0	0	0
17	1	0	smooth	0	false	false	x	0	0	0	0	0
19	1	1	cusp	1	false	false	x	0	1	1	1	1
23	2	0	smooth	0	false	false	x	0	0	0	0	0
29	2	0	smooth	0	false	false	x	0	0	0	0	0
31	2	0	smooth	0	false	false	x	0	0	0	0	0
37	2	1	cusp	1	false	false	x	0	2	2	2	2
41	3	0	smooth	0	false	false	x	0	0	0	0	0
43	3	0	smooth	0	false	false	x	0	0	0	0	0
47	4	0	smooth	0	false	false	x	0	0	0	0	0
53	4	0	smooth	0	false	false	x	0	0	0	0	0
59	5	0	smooth	0	false	false	x	0	0	0	0	0
61	4	0	smooth	0	false	false	x	0	0	0	0	0
67	5	0	smooth	0	false	false	x	0	0	0	0	0
71	6	2	non-split node	2	false	false	x^2	1	1	3	3	9
73	5	1	cusp	1	false	false	x	0	2	4	7	7
79	6	0	smooth	0	false	false	x	0	0	0	0	0
83	7	0	smooth	0	false	false	x	0	0	0	0	0
89	7	0	smooth	0	false	false	x	0	0	0	0	0
97	7	0	smooth	0	false	false	x	0	0	0	0	0
101	8	1	cusp	1	false	false	x	0	1	1	1	1
103	8	0	smooth	0	false	false	x	0	0	0	0	0
107	9	0	smooth	0	false	false	x	0	0	0	0	0
109	8	1	cusp	1	false	false	x	0	2	2	2	2
113	9	1	cusp	1	false	false	x	0	3	7	7	13
127	10	3	split node	3	true	true	x^2	1	1	3	3	3
131	11	1	cusp	1	false	false	x	0	1	1	1	1
137	11	0	smooth	0	false	false	x	0	0	0	0	0
139	11	0	smooth	0	false	false	x	0	0	0	0	0
149	12	1	cusp	1	false	false	x	0	1	1	1	1
151	12	1	cusp	1	false	false	x	0	1	1	1	1
157	12	0	smooth	0	false	false	x	0	0	0	0	0
163	13	3	split node	3	true	true	x^2	1	1	3	9	18
167	14	2	cusp	2	false	false	x	0	1	3	0	0
173	14	0	smooth	0	false	false	x	0	0	0	0	0
179	15	0	smooth	0	false	false	x	0	0	0	0	0
181	14	1	cusp	1	false	false	x	0	1	1	1	1
191	16	0	smooth	0	false	false	x	0	0	0	0	0
193	15	0	smooth	0	false	false	x	0	0	0	0	0
197	16	0	smooth	0	false	false	x	0	0	0	0	0
199	16	4	split node	4	true	true	x^2	1	1	3	9	0
211	17	0	smooth	0	false	false	x	0	0	0	0	0
223	18	1	cusp	1	false	false	x	0	1	1	1	1
227	19	0	smooth	0	false	false	x	0	0	0	0	0
229	18	0	smooth	0	false	false	x	0	0	0	0	0
233	19	0	smooth	0	false	false	x	0	0	0	0	0
239	20	0	smooth	0	false	false	x	0	0	0	0	0
241	19	0	smooth	0	false	false	x	0	0	0	0	0
251	21	0	smooth	0	false	false	x	0	0	0	0	0
257	21	0	smooth	0	false	false	x	0	0	0	0	0
263	22	0	smooth	0	false	false	x	0	0	0	0	0
269	22	2	non-split node	2	false	false	x^2	1	1	3	6	6
271	22	2	non-split node	2	false	false	x^2	1	1	3	6	6
277	22	0	smooth	0	false	false	x	0	0	0	0	0
281	23	0	smooth	0	false	false	x	0	0	0	0	0
283	23	0	smooth	0	false	false	x	0	0	0	0	0
293	24	1	cusp	1	false	false	x	0	1	1	1	1
307	25	2	split node	2	true	true	x	0	3	7	16	25
311	26	0	smooth	0	false	false	x	0	0	0	0	0
313	25	0	smooth	0	false	false	x	0	0	0	0	0
317	26	0	smooth	0	false	false	x	0	0	0	0	0
331	27	0	smooth	0	false	false	x	0	0	0	0	0
337	27	3	split node	3	true	true	x	0	1	3	9	18
347	29	0	smooth	0	false	false	x	0	0	0	0	0
349	28	0	smooth	0	false	false	x	0	0	0	0	0
353	29	0	smooth	0	false	false	x	0	0	0	0	0
359	30	2	non-split node	2	false	false	x^2	1	3	4	4	4
367	30	0	smooth	0	false	false	x	0	0	0	0	0
373	30	0	smooth	0	false	false	x	0	0	0	0	0
379	31	1	cusp	1	false	false	x	0	1	1	1	1
383	32	1	cusp	1	false	false	x	0	1	1	1	1
389	32	0	smooth	0	false	false	x	0	0	0	0	0
397	32	1	cusp	1	false	false	x	0	2	2	2	2
401	33	0	smooth	0	false	false	x	0	0	0	0	0
409	33	0	smooth	0	false	false	x	0	0	0	0	0
419	35	0	smooth	0	false	false	x	0	0	0	0	0
421	34	2	non-split node	2	false	false	x^2	1	1	0	0	0
431	36	1	cusp	1	false	false	x	0	3	5	5	11
433	35	1	cusp	1	false	false	x	0	3	5	11	29
439	36	4	non-split node	4	false	false	x^2	2	3	9	3	9
443	37	2	non-split node	2	false	false	x^2	1	3	9	24	42
449	37	5	split node	5	true	true	x^2	1	1	3	9	27
457	37	0	smooth	0	false	false	x	0	0	0	0	0
461	38	0	smooth	0	false	false	x	0	0	0	0	0
463	38	1	cusp	1	false	false	x	0	1	1	1	1
467	39	1	cusp	1	false	false	x	0	1	1	1	1
479	40	0	smooth	0	false	false	x	0	0	0	0	0
487	40	7	split node	7	true	true	x^2	2	1	3	9	27
491	41	0	smooth	0	false	false	x	0	0	0	0	0
499	41	6	split node	6	true	true	x^2	2	2	6	12	36
503	42	1	cusp	1	false	false	x	0	3	7	13	19
509	42	2	non-split node	2	false	false	x^2	1	1	0	0	0
521	43	1	cusp	1	false	false	x	0	1	1	1	1
523	43	2	non-split node	2	false	false	x^2	1	1	0	0	0
541	44	4	split node	4	true	true	x^2	1	1	3	9	27
547	45	0	smooth	0	false	false	x	0	0	0	0	0
557	46	2	cusp	2	false	false	x	0	3	5	5	11
563	47	0	smooth	0	false	false	x	0	0	0	0	0
569	47	0	smooth	0	false	false	x	0	0	0	0	0
571	47	2	non-split node	2	false	false	x^2	1	2	6	15	33
577	47	3	split node	3	true	true	x^2	1	1	3	9	27
587	49	1	cusp	1	false	false	x	0	1	1	1	1
593	49	1	cusp	1	false	false	x	0	3	5	8	8
599	50	1	cusp	1	false	false	x	0	1	1	1	1
601	49	2	non-split node	2	false	false	x^2	1	1	0	0	0
607	50	0	smooth	0	false	false	x	0	0	0	0	0
613	50	1	cusp	1	false	false	x	0	1	1	1	1
617	51	0	smooth	0	false	false	x	0	0	0	0	0
619	51	2	cusp	2	false	false	x	0	1	3	0	0
631	52	5	split node	5	true	true	x^2	2	1	3	9	9
641	53	0	smooth	0	false	false	x	0	0	0	0	0
643	53	0	smooth	0	false	false	x	0	0	0	0	0
647	54	0	smooth	0	false	false	x	0	0	0	0	0
653	54	0	smooth	0	false	false	x	0	0	0	0	0
659	55	1	cusp	1	false	false	x	0	3	5	8	8
661	54	0	smooth	0	false	false	x	0	0	0	0	0
673	55	0	smooth	0	false	false	x	0	0	0	0	0
677	56	0	smooth	0	false	false	x	0	0	0	0	0
683	57	0	smooth	0	false	false	x	0	0	0	0	0
691	57	0	smooth	0	false	false	x	0	0	0	0	0
701	58	0	smooth	0	false	false	x	0	0	0	0	0
709	58	0	smooth	0	false	false	x	0	0	0	0	0
719	60	0	smooth	0	false	false	x	0	0	0	0	0
727	60	1	cusp	1	false	false	x	0	1	1	1	1
733	60	0	smooth	0	false	false	x	0	0	0	0	0
739	61	1	cusp	1	false	false	x	0	2	4	4	10
743	62	0	smooth	0	false	false	x	0	0	0	0	0
751	62	2	cusp	2	false	false	x	0	1	3	0	0
757	62	1	cusp	1	false	false	x	0	2	2	2	2
761	63	2	cusp	2	false	false	x	0	2	6	6	18
769	63	0	smooth	0	false	false	x	0	0	0	0	0
773	64	3	split node	3	true	true	x	0	3	9	21	45
787	65	0	smooth	0	false	false	x	0	0	0	0	0
797	66	0	smooth	0	false	false	x	0	0	0	0	0
809	67	0	smooth	0	false	false	x	0	0	0	0	0
811	67	3	split node	3	true	true	x^2	1	1	3	9	27
821	68	0	smooth	0	false	false	x	0	0	0	0	0
823	68	0	smooth	0	false	false	x	0	0	0	0	0
827	69	1	cusp	1	false	false	x	0	1	1	1	1
829	68	3	split node	3	true	true	x^2	1	2	6	9	18
839	70	0	smooth	0	false	false	x	0	0	0	0	0
853	70	0	smooth	0	false	false	x	0	0	0	0	0
857	71	5	split node	5	true	true	x^2	2	1	3	9	9
859	71	0	smooth	0	false	false	x	0	0	0	0	0
863	72	0	smooth	0	false	false	x	0	0	0	0	0
877	72	0	smooth	0	false	false	x	0	0	0	0	0
881	73	0	smooth	0	false	false	x	0	0	0	0	0
883	73	3	split node	3	true	true	x	0	2	4	10	10
887	74	0	smooth	0	false	false	x	0	0	0	0	0
907	75	0	smooth	0	false	false	x	0	0	0	0	0
911	76	0	smooth	0	false	false	x	0	0	0	0	0
919	76	4	split node	4	true	true	x	0	2	6	9	27
929	77	0	smooth	0	false	false	x	0	0	0	0	0
937	77	1	cusp	1	false	false	x	0	1	1	1	1
941	78	1	cusp	1	false	false	x	0	1	1	1	1
947	79	2	non-split node	2	false	false	x^2	1	1	0	0	0
953	79	1	cusp	1	false	false	x	0	1	1	1	1
967	80	0	smooth	0	false	false	x	0	0	0	0	0
971	81	0	smooth	0	false	false	x	0	0	0	0	0
977	81	0	smooth	0	false	false	x	0	0	0	0	0
983	82	0	smooth	0	false	false	x	0	0	0	0	0
991	82	1	cusp	1	false	false	x	0	1	1	1	1
997	82	2	non-split node	2	false	false	x^2	1	2	6	15	24

Totals

Total levels: 164 - smooth: 95 - cusp: 39 - split node: 17 - non-split node: 13

qdim >= 2 block

level	dim S2	qdim	category	alg_dim	idemp_mod3	lift_z3	T2 rank
71	6	2	non-split node	2	false	false	1
127	10	3	split node	3	true	true	1
163	13	3	split node	3	true	true	1
167	14	2	cusp	2	false	false	0
199	16	4	split node	4	true	true	1
269	22	2	non-split node	2	false	false	1
271	22	2	non-split node	2	false	false	1
307	25	2	split node	2	true	true	0
337	27	3	split node	3	true	true	0
359	30	2	non-split node	2	false	false	1
421	34	2	non-split node	2	false	false	1
439	36	4	non-split node	4	false	false	2
443	37	2	non-split node	2	false	false	1
449	37	5	split node	5	true	true	1
487	40	7	split node	7	true	true	2
499	41	6	split node	6	true	true	2
509	42	2	non-split node	2	false	false	1
523	43	2	non-split node	2	false	false	1
541	44	4	split node	4	true	true	1
557	46	2	cusp	2	false	false	0
571	47	2	non-split node	2	false	false	1
577	47	3	split node	3	true	true	1
601	49	2	non-split node	2	false	false	1
619	51	2	cusp	2	false	false	0
631	52	5	split node	5	true	true	2
751	62	2	cusp	2	false	false	0
761	63	2	cusp	2	false	false	0
773	64	3	split node	3	true	true	0
811	67	3	split node	3	true	true	1
829	68	3	split node	3	true	true	1
857	71	5	split node	5	true	true	2
883	73	3	split node	3	true	true	0
919	76	4	split node	4	true	true	0
947	79	2	non-split node	2	false	false	1
997	82	2	non-split node	2	false	false	1