C8 overview

C₈ · Neutral gradings

100 neutral gradings · KL, Fourier, Arthur packets

Ambient orbit	KL block sizes	Arthur parameters	Parameters in packets	Graded orbits	Local systems
1111111111111111	1 × 1	1	1	1	1
211111111111111	2 × 2, 1 × 1	2	3	2	3
22111111111111	4 × 4, 1 × 1	3	5	3	5
2221111111111	5 × 5, 2 × 2	4	7	4	7
4111111111111	4 × 4, 2 × 2	2	4	4	6
222211111111	7 × 7, 2 × 2	5	9	5	9
331111111111	4 × 4	3	3	4	4
421111111111	10 × 10, 4 × 4, 1 × 1	6	13	8	15
22222111111	8 × 8, 3 × 3	6	11	6	11
33211111111	8 × 8, 4 × 4	6	9	8	12
2222221111	10 × 10, 3 × 3	7	13	7	13
42211111111	16 × 16, 8 × 8, 1 × 1	10	23	12	25
61111111111	8 × 8, 4 × 4	2	4	8	12
222222211	11 × 11, 4 × 4	8	15	8	15
22222222	13 × 13, 4 × 4	9	17	9	17
3322111111	16 × 16, 4 × 4	9	15	12	20
4222111111	23 × 23, 10 × 10, 2 × 2	14	33	16	35
4411111111	14 × 14, 5 × 5, 1 × 1	3	8	11	20
332221111	20 × 20, 8 × 8	12	21	16	28
6211111111	20 × 20, 8 × 8, 2 × 2	4	12	16	30
422221111	29 × 29, 14 × 14, 2 × 2	18	43	20	45
33222211	28 × 28, 8 × 8	15	27	20	36
433111111	16 × 16, 8 × 8	6	12	16	24
3322222	24 × 24, 9 × 9	12	22	18	33
33331111	9 × 9	6	6	9	9
42222211	36 × 36, 16 × 16, 3 × 3	22	53	24	55
442111111	27 × 27, 14 × 14, 2 × 2	10	29	20	43
4222222	42 × 42, 20 × 20, 3 × 3	26	63	28	65
622111111	32 × 32, 16 × 16, 2 × 2	6	20	24	50
3333211	16 × 16, 8 × 8	10	15	16	24
43321111	40 × 40, 16 × 16, 4 × 4	18	39	32	60
811111111	16 × 16, 8 × 8	2	4	16	24
333322	24 × 24, 6 × 6	9	15	18	30
44221111	46 × 46, 20 × 20, 4 × 4	20	56	30	70
4332211	64 × 64, 32 × 32, 4 × 4	30	69	48	100
55111111	13 × 13	2	2	13	13
62221111	46 × 46, 20 × 20, 4 × 4	8	28	32	70
433222	69 × 69, 30 × 30, 6 × 6	28	66	48	105
4422211	62 × 62, 31 × 31, 5 × 5	30	84	40	98
64111111	36 × 36, 15 × 15, 4 × 4	6	18	29	55
43333	24 × 24, 12 × 12	6	12	24	36
442222	82 × 82, 37 × 37, 7 × 7	40	112	50	126
4441111	32 × 32, 16 × 16, 2 × 2	4	12	24	50
6222211	58 × 58, 28 × 28, 4 × 4	10	36	40	90
82111111	40 × 40, 16 × 16, 4 × 4	4	12	32	60
443311	56 × 56, 20 × 20, 4 × 4	9	24	44	80
5521111	26 × 26, 13 × 13	4	6	26	39
622222	72 × 72, 32 × 32, 6 × 6	12	44	48	110
6331111	32 × 32, 16 × 16	6	12	32	48
44332	81 × 81, 42 × 42, 6 × 6	20	58	60	129
444211	62 × 62, 28 × 28, 6 × 6	14	47	41	96
6421111	73 × 73, 40 × 40, 8 × 8, 1 × 1	18	61	54	122
44422	95 × 95, 48 × 48, 8 × 8	30	99	60	151
552211	52 × 52, 13 × 13	6	10	39	65
633211	80 × 80, 32 × 32, 8 × 8	12	36	64	120
8221111	64 × 64, 32 × 32, 4 × 4	6	20	48	100
(10,1,1,1,1,1,1)	32 × 32, 16 × 16	2	4	32	48
4444	69 × 69, 30 × 30, 6 × 6	5	16	46	105
55222	50 × 50, 20 × 20	8	14	40	70
63322	96 × 96, 48 × 48, 6 × 6	12	40	72	150
642211	123 × 123, 60 × 60, 16 × 16, 1 × 1	30	111	81	200
5533	32 × 32	6	6	32	32
55411	52 × 52, 26 × 26	4	8	52	78
64222	168 × 168, 90 × 90, 20 × 20, 2 × 2	42	161	108	280
661111	50 × 50, 20 × 20, 5 × 5	3	8	40	75
822211	92 × 92, 40 × 40, 8 × 8	8	28	64	140
5542	100 × 100, 40 × 40, 10 × 10	12	26	80	150
6433	108 × 108, 45 × 45, 12 × 12	12	36	87	165
64411	100 × 100, 54 × 54, 10 × 10, 1 × 1	10	39	74	165
82222	116 × 116, 56 × 56, 8 × 8	10	36	80	180
841111	72 × 72, 30 × 30, 8 × 8	4	16	58	110
(10,2,1,1,1,1)	80 × 80, 32 × 32, 8 × 8	4	12	64	120
6442	200 × 200, 100 × 100, 28 × 28, 2 × 2	36	148	130	330
66211	100 × 100, 54 × 54, 10 × 10, 1 × 1	6	24	74	165
83311	64 × 64, 32 × 32	6	12	64	96
655	80 × 80, 40 × 40	4	8	80	120
6622	169 × 169, 80 × 80, 20 × 20, 1 × 1	9	40	111	270
8332	120 × 120, 48 × 48, 12 × 12	8	24	96	180
84211	146 × 146, 80 × 80, 16 × 16, 2 × 2	12	52	108	244
(10,2,2,1,1)	128 × 128, 64 × 64, 8 × 8	6	20	96	200
664	168 × 168, 92 × 92, 18 × 18, 2 × 2	10	40	124	280
7711	45 × 45	2	2	45	45
8422	246 × 246, 120 × 120, 32 × 32, 2 × 2	20	92	162	400
(10,2,2,2)	184 × 184, 80 × 80, 16 × 16	8	28	128	280
(12,1,1,1,1)	64 × 64, 32 × 32	2	4	64	96
772	70 × 70, 35 × 35	4	6	70	105
844	200 × 200, 108 × 108, 20 × 20, 2 × 2	6	32	148	330
8611	130 × 130, 55 × 55, 15 × 15	6	18	105	200
(10,3,3)	96 × 96, 48 × 48	4	8	96	144
(10,4,1,1)	144 × 144, 60 × 60, 16 × 16	4	16	116	220
862	265 × 265, 146 × 146, 30 × 30, 4 × 4	12	54	196	445
(10,4,2)	292 × 292, 160 × 160, 32 × 32, 4 × 4	12	52	216	488
(12,2,1,1)	160 × 160, 64 × 64, 16 × 16	4	12	128	240
88	180 × 180, 75 × 75, 20 × 20	3	8	145	275
(10,6)	260 × 260, 110 × 110, 30 × 30	4	16	210	400
(12,2,2)	256 × 256, 128 × 128, 16 × 16	6	20	192	400
(12,4)	288 × 288, 120 × 120, 32 × 32	4	16	232	440
(14,1,1)	128 × 128, 64 × 64	2	4	128	192
(14,2)	320 × 320, 128 × 128, 32 × 32	4	12	256	480
(16)	256 × 256, 128 × 128	2	4	256	384

Counting conventions

Matrix dimensions are listed separately for each block. Parameters in packets counts distinct IC parameters, without multiplicities or repeated membership. Local systems counts orbit–local-system pairs across all exported series. “Not computed” means that the selected export does not contain that result, rather than a count of zero.