Prime-Level Census: Singular 3-adic Hecke Nodes

Scan primes N <= 500.

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

Totals

Total levels: 91 - smooth: 56 - cusp: 20 - split node: 8 - non-split node: 7

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