B9 overview

B₉ · Neutral gradings

130 neutral gradings · KL, Fourier, Arthur packets

Ambient orbit	KL block sizes	Arthur parameters	Parameters in packets	Graded orbits	Local systems
1111111111111111111	1 × 1	1	1	1	1
22111111111111111	2 × 2	2	2	2	2
31111111111111111	4 × 4	3	4	3	4
222211111111111	3 × 3	3	3	3	3
322111111111111	8 × 8	6	8	6	8
331111111111111	9 × 9	6	9	6	9
511111111111111	8 × 8	2	4	6	8
2222221111111	4 × 4	4	4	4	4
3222211111111	12 × 12	9	12	9	12
22222222111	5 × 5	5	5	5	5
3322111111111	18 × 18	12	18	12	18
3331111111111	16 × 16	10	16	10	16
4411111111111	6 × 6	2	2	6	6
5221111111111	16 × 16	4	8	12	16
32222221111	16 × 16	12	16	12	16
5311111111111	25 × 25, 1 × 1	9	19	16	26
322222222	10 × 10, 1 × 1	10	11	10	11
7111111111111	16 × 16	2	4	12	16
33222211111	27 × 27	18	27	18	27
332222221	28 × 28, 1 × 1	20	29	20	29
33322111111	32 × 32	20	32	20	32
33331111111	25 × 25	15	25	15	25
52222111111	24 × 24	6	12	18	24
44221111111	13 × 13	6	6	13	13
333222211	42 × 42, 1 × 1	27	43	27	43
44311111111	24 × 24	6	8	18	24
53221111111	50 × 50, 2 × 2	18	38	32	52
522222211	32 × 32	8	16	24	32
53311111111	54 × 54, 2 × 2	21	46	31	56
333322111	46 × 46, 1 × 1	28	47	28	47
55111111111	34 × 34, 1 × 1	3	8	22	35
72211111111	32 × 32	4	8	24	32
333331111	34 × 34, 1 × 1	20	35	20	35
442222111	20 × 20	10	10	20	20
73111111111	50 × 50, 2 × 2	6	16	32	52
3333322	36 × 36	12	20	24	36
532222111	75 × 75, 3 × 3	27	57	48	78
91111111111	32 × 32	2	4	24	32
3333331	31 × 31	13	23	19	31
443221111	52 × 52	18	24	39	52
4432222	40 × 40, 2 × 2	20	22	40	42
443311111	54 × 54	12	18	36	54
533221111	108 × 108, 4 × 4	42	92	62	112
5332222	81 × 81, 3 × 3, 2 × 2	30	59	57	86
533311111	94 × 94, 4 × 4	38	85	51	98
722221111	48 × 48	6	12	36	48
4433221	91 × 91, 2 × 2	30	44	65	93
544111111	48 × 48	4	8	36	48
552211111	68 × 68, 2 × 2	6	16	44	70
7222222	32 × 32, 2 × 2	8	10	32	34
4433311	84 × 84, 2 × 2	18	30	54	86
5333221	132 × 132, 6 × 6, 2 × 2	54	116	78	140
553111111	92 × 92, 4 × 4	15	44	52	96
732211111	100 × 100, 4 × 4	12	32	64	104
4444111	20 × 20	3	3	20	20
5333311	118 × 118, 5 × 5, 2 × 2	49	110	64	125
5522221	81 × 81, 3 × 3	9	24	57	84
661111111	20 × 20	2	2	20	20
733111111	108 × 108, 4 × 4	12	36	62	112
44443	40 × 40, 3 × 3	6	9	40	43
5442211	104 × 104	12	24	78	104
7322221	120 × 120, 6 × 6, 4 × 4	18	46	84	130
751111111	91 × 91, 4 × 4	6	18	58	95
922111111	64 × 64	4	8	48	64
5443111	150 × 150, 6 × 6	18	38	96	156
5532211	168 × 168, 8 × 8	30	88	98	176
931111111	100 × 100, 4 × 4	6	16	64	104
(11,1,1,1,1,1,1,1,1)	64 × 64	2	4	48	64
54433	162 × 162, 6 × 6, 4 × 4	20	42	114	172
5533111	179 × 179, 9 × 9	42	120	94	188
7332211	196 × 196, 8 × 8, 4 × 4	24	72	116	208
55333	160 × 160, 8 × 8, 3 × 3	30	81	92	171
5551111	108 × 108, 4 × 4	4	12	62	112
6622111	44 × 44	4	4	44	44
7333111	178 × 178, 8 × 8, 4 × 4	20	66	98	190
9222211	96 × 96	6	12	72	96
55441	162 × 162, 6 × 6	6	16	114	168
55522	108 × 108, 4 × 4	8	12	76	112
6631111	80 × 80	6	8	60	80
73333	146 × 146, 6 × 6	10	32	88	152
7441111	96 × 96	4	8	72	96
7522111	182 × 182, 8 × 8	12	36	116	190
55531	183 × 183, 10 × 10	21	61	104	193
66322	88 × 88, 4 × 4	8	10	88	92
74422	104 × 104, 4 × 4	12	16	104	108
7531111	252 × 252, 16 × 16	27	90	140	268
9322111	200 × 200, 8 × 8	12	32	128	208
66331	140 × 140, 3 × 3	10	16	100	143
74431	240 × 240, 12 × 12, 8 × 8	12	36	168	260
75322	252 × 252, 16 × 16, 8 × 8	36	92	174	276
7711111	125 × 125, 5 × 5	3	8	80	130
9331111	216 × 216, 8 × 8	12	36	124	224
(11,2,2,1,1,1,1)	128 × 128	4	8	96	128
66511	160 × 160	4	8	120	160
75331	373 × 373, 28 × 28, 10 × 10	54	180	208	411
93322	216 × 216, 8 × 8, 4 × 4	12	32	152	228
9511111	182 × 182, 8 × 8	4	16	116	190
(11,2,2,2,2)	96 × 96, 4 × 4	6	8	96	100
(11,3,1,1,1,1,1)	200 × 200, 8 × 8	6	16	128	208
75511	316 × 316, 20 × 20	10	40	182	336
77221	200 × 200, 10 × 10, 5 × 5	6	17	140	215
93331	264 × 264, 12 × 12, 4 × 4	14	44	156	280
(13,1,1,1,1,1,1)	128 × 128	2	4	96	128
766	160 × 160, 6 × 6	4	8	160	166
77311	316 × 316, 20 × 20, 7 × 7	9	33	182	343
94411	192 × 192	4	8	144	192
95221	292 × 292, 16 × 16, 1 × 1	8	33	204	309
(11,3,2,2,1)	320 × 320, 16 × 16, 8 × 8	12	32	224	344
775	290 × 290, 18 × 18, 10 × 10	10	26	200	318
88111	70 × 70	2	2	70	70
95311	464 × 464, 32 × 32, 1 × 1	18	77	266	497
(11,3,3,1,1)	392 × 392, 16 × 16, 8 × 8	12	38	232	416
883	140 × 140, 6 × 6	4	6	140	146
955	344 × 344, 20 × 20, 1 × 1	6	17	238	365
97111	330 × 330, 15 × 15	6	18	210	345
(11,4,4)	192 × 192, 8 × 8	4	8	192	200
(11,5,1,1,1)	364 × 364, 16 × 16	4	16	232	380
(13,2,2,1,1)	256 × 256	4	8	192	256
973	458 × 458, 30 × 30, 16 × 16	12	40	316	504
(11,5,3)	504 × 504, 32 × 32, 16 × 16	12	44	348	552
(13,3,1,1,1)	400 × 400, 16 × 16	6	16	256	416
991	365 × 365, 20 × 20, 1 × 1	3	9	255	386
(11,7,1)	530 × 530, 30 × 30, 15 × 15	4	20	370	575
(13,3,3)	432 × 432, 16 × 16, 8 × 8	6	16	304	456
(15,1,1,1,1)	256 × 256	2	4	192	256
(13,5,1)	584 × 584, 32 × 32, 2 × 2	4	18	408	618
(15,2,2)	256 × 256, 8 × 8	4	6	256	264
(15,3,1)	640 × 640, 32 × 32, 16 × 16	6	18	448	688
(17,1,1)	512 × 512	2	4	384	512
(19)	512 × 512, 16 × 16	2	4	512	528

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.