B8 overview

B₈ · Neutral gradings

86 neutral gradings · KL, Fourier, Arthur packets

Ambient orbit	KL block sizes	Arthur parameters	Parameters in packets	Graded orbits	Local systems
11111111111111111	1 × 1	1	1	1	1
221111111111111	2 × 2	2	2	2	2
311111111111111	4 × 4	3	4	3	4
2222111111111	3 × 3	3	3	3	3
3221111111111	8 × 8	6	8	6	8
3311111111111	9 × 9	6	9	6	9
5111111111111	8 × 8	2	4	6	8
22222211111	4 × 4	4	4	4	4
222222221	5 × 5, 1 × 1	5	6	5	6
32222111111	12 × 12	9	12	9	12
33221111111	18 × 18	12	18	12	18
322222211	16 × 16, 1 × 1	12	17	12	17
33311111111	16 × 16	10	16	10	16
44111111111	6 × 6	2	2	6	6
52211111111	16 × 16	4	8	12	16
53111111111	25 × 25, 1 × 1	9	19	16	26
332222111	27 × 27, 1 × 1	18	28	18	28
71111111111	16 × 16	2	4	12	16
333221111	32 × 32, 1 × 1	20	33	20	33
3332222	24 × 24	12	18	18	24
333311111	25 × 25, 1 × 1	15	26	15	26
522221111	24 × 24	6	12	18	24
442211111	13 × 13	6	6	13	13
5222222	16 × 16, 2 × 2	8	10	16	18
3333221	34 × 34	18	30	22	34
443111111	24 × 24	6	8	18	24
532211111	50 × 50, 2 × 2	18	38	32	52
3333311	28 × 28	15	26	17	28
4422221	20 × 20, 2 × 2	10	12	20	22
533111111	54 × 54, 2 × 2	21	46	31	56
5322221	60 × 60, 3 × 3, 4 × 4	27	52	42	67
551111111	34 × 34, 1 × 1	3	8	22	35
722111111	32 × 32	4	8	24	32
4432211	52 × 52, 2 × 2	18	26	39	54
731111111	50 × 50, 2 × 2	6	16	32	52
4433111	54 × 54, 2 × 2	12	20	36	56
5332211	98 × 98, 4 × 4, 4 × 4	42	90	58	106
911111111	32 × 32	2	4	24	32
44333	48 × 48	8	12	36	48
5333111	89 × 89, 4 × 4, 4 × 4	38	86	49	97
7222211	48 × 48, 2 × 2	6	12	36	50
44441	20 × 20, 3 × 3	3	6	20	23
53333	73 × 73, 3 × 3	18	41	44	76
5441111	48 × 48	4	8	36	48
5522111	68 × 68, 2 × 2	6	16	44	70
54422	52 × 52, 4 × 4	12	16	52	56
5531111	92 × 92, 4 × 4	15	44	52	96
7322111	100 × 100, 4 × 4, 2 × 2	12	32	64	106
54431	120 × 120, 6 × 6, 8 × 8	18	40	84	134
55322	92 × 92, 4 × 4, 5 × 5	20	45	64	101
6611111	20 × 20	2	2	20	20
7331111	108 × 108, 4 × 4, 2 × 2	12	36	62	114
55331	134 × 134, 7 × 7, 7 × 7	36	96	76	148
73322	108 × 108, 4 × 4	12	32	76	112
7511111	91 × 91, 4 × 4	6	18	58	95
9221111	64 × 64	4	8	48	64
55511	98 × 98, 4 × 4	4	12	58	102
66221	44 × 44, 4 × 4	4	6	44	48
73331	132 × 132, 6 × 6	14	44	78	138
92222	48 × 48, 4 × 4	6	8	48	52
9311111	100 × 100, 4 × 4	6	16	64	104
(11,1,1,1,1,1,1)	64 × 64	2	4	48	64
66311	80 × 80, 3 × 3	6	10	60	83
74411	96 × 96, 4 × 4	4	8	72	100
75221	146 × 146, 8 × 8, 8 × 8	12	40	102	162
665	80 × 80, 6 × 6	4	8	80	86
75311	232 × 232, 16 × 16, 10 × 10	27	96	133	258
93221	160 × 160, 8 × 8, 8 × 8	12	32	112	176
755	172 × 172, 10 × 10, 10 × 10	10	26	119	192
77111	125 × 125, 5 × 5, 3 × 3	3	8	80	133
93311	196 × 196, 8 × 8, 8 × 8	12	38	116	212
(11,2,2,1,1)	128 × 128, 4 × 4	4	8	96	132
773	172 × 172, 10 × 10	6	16	119	182
944	96 × 96, 8 × 8	4	8	96	104
95111	182 × 182, 8 × 8	4	16	116	190
(11,3,1,1,1)	200 × 200, 8 × 8, 4 × 4	6	16	128	212
881	70 × 70, 6 × 6	2	4	70	76
953	252 × 252, 16 × 16, 15 × 15	12	44	174	283
(11,3,3)	216 × 216, 8 × 8	6	16	152	224
(13,1,1,1,1)	128 × 128	2	4	96	128
971	265 × 265, 15 × 15, 16 × 16	6	24	185	296
(11,5,1)	292 × 292, 16 × 16, 16 × 16	4	18	204	324
(13,2,2)	128 × 128, 8 × 8	4	6	128	136
(13,3,1)	320 × 320, 16 × 16, 16 × 16	6	18	224	352
(15,1,1)	256 × 256, 8 × 8	2	4	192	264
(17)	256 × 256, 16 × 16	2	4	256	272

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.