[Introduction] - Groups of Genus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Congruence Subgroups of PSL(2,Z)

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^ Statistics

The table below gives the number of congruence subgroups of genus 0 to 24, giving the total number, the number of congruence subgroups up to conjugacy in PSL(2,Z) and PGL(2,Z), and the maximal index and maximal level for each genus. The same is data is also given for the torsion-free subgroups (the groups with c₂=c₃=0 in the main tables) and the cycloidal subgroups (the groups with one equivalence class of cusps).
 

	All Groups					Torsion Free Groups					Cycloidal Groups
Genus	#All	#PSL	#PGL	Max. Level	Max. Index	#All	#PSL	#PGL	Max. Level	Max. Index	#All	#PSL	#PGL	Max. Level	Max. Index
0	1116	132	121	48	72	254	33	33	32	60	151	26	18	21	21
1	2801	187	163	52	108	459	48	48	36	108	311	25	16	42	42
2	4107	177	145	78	108	672	49	49	64	108	410	14	8	63	63
3	6513	284	241	96	168	1809	108	105	72	168	638	24	13	84	84
4	7257	261	215	108	180	1665	87	86	81	180	824	21	11	80	80
5	9386	303	256	126	192	3028	133	125	75	192	696	12	6	126	126
6	10416	230	175	126	192	1780	55	45	121	180	378	10	5	126	126
7	18191	480	388	156	216	6216	213	191	128	216	1057	22	12	132	132
8	13726	277	212	169	220	2671	83	76	96	156	675	9	5	126	126
9	21014	469	403	154	288	6711	208	203	128	288	468	8	4	154	154
10	15622	304	235	168	324	4483	133	120	118	324	1972	30	15	168	168
11	27466	489	381	198	288	8450	195	179	147	240	874	10	5	198	198
12	18095	269	198	210	330	4978	93	70	142	300	418	6	3	165	165
13	33241	664	549	231	384	12447	343	303	162	384	628	9	5	231	231
14	22871	268	178	252	300	4581	72	53	167	192	1098	6	3	252	252
15	40880	596	485	240	384	16743	289	263	179	288	440	8	4	240	240
16	30809	410	294	243	364	8607	143	123	243	360	930	10	5	220	220
17	54794	819	667	289	480	17453	351	317	242	480	478	6	3	210	210
18	24935	273	191	264	384	4819	71	60	214	288	774	10	5	264	264
19	60648	812	647	273	504	24287	411	375	256	504	320	4	2	240	240
20	31137	308	203	286	408	9396	122	85	239	300	0	0	0	0	0
21	66841	888	729	308	480	27542	504	450	256	480	2352	12	6	308	308
22	36135	365	284	361	486	11206	152	132	263	432	0	0	0	0	0
23	59450	686	537	338	504	22798	312	271	274	384	630	2	1	315	315
24	42289	336	212	336	546	6903	78	51	284	336	2232	22	11	336	336
All	659740	10287	8109	361	546	209958	4286	3813	284	504	18754	306	166	336	336