B₇ · Neutral gradings
55 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 111111111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 2211111111111 | 2 × 2 | 2 | 2 | 2 | 2 |
| 3111111111111 | 4 × 4 | 3 | 4 | 3 | 4 |
| 22221111111 | 3 × 3 | 3 | 3 | 3 | 3 |
| 32211111111 | 8 × 8 | 6 | 8 | 6 | 8 |
| 33111111111 | 9 × 9 | 6 | 9 | 6 | 9 |
| 222222111 | 4 × 4 | 4 | 4 | 4 | 4 |
| 51111111111 | 8 × 8 | 2 | 4 | 6 | 8 |
| 322221111 | 12 × 12 | 9 | 12 | 9 | 12 |
| 3222222 | 8 × 8, 1 × 1 | 8 | 9 | 8 | 9 |
| 332211111 | 18 × 18 | 12 | 18 | 12 | 18 |
| 333111111 | 16 × 16 | 10 | 16 | 10 | 16 |
| 3322221 | 21 × 21, 1 × 1 | 15 | 22 | 15 | 22 |
| 441111111 | 6 × 6 | 2 | 2 | 6 | 6 |
| 522111111 | 16 × 16 | 4 | 8 | 12 | 16 |
| 531111111 | 25 × 25, 1 × 1 | 9 | 19 | 16 | 26 |
| 3332211 | 28 × 28, 1 × 1 | 18 | 29 | 18 | 29 |
| 711111111 | 16 × 16 | 2 | 4 | 12 | 16 |
| 3333111 | 23 × 23, 1 × 1 | 14 | 24 | 14 | 24 |
| 5222211 | 24 × 24 | 6 | 12 | 18 | 24 |
| 33333 | 18 × 18 | 6 | 10 | 12 | 18 |
| 4422111 | 13 × 13 | 6 | 6 | 13 | 13 |
| 4431111 | 24 × 24 | 6 | 8 | 18 | 24 |
| 5322111 | 50 × 50, 2 × 2 | 18 | 38 | 32 | 52 |
| 44322 | 26 × 26, 2 × 2 | 12 | 14 | 26 | 28 |
| 5331111 | 54 × 54, 2 × 2 | 21 | 46 | 31 | 56 |
| 44331 | 42 × 42, 2 × 2 | 10 | 16 | 30 | 44 |
| 53322 | 54 × 54, 2 × 2, 2 × 2 | 20 | 40 | 38 | 58 |
| 5511111 | 34 × 34, 1 × 1 | 3 | 8 | 22 | 35 |
| 7221111 | 32 × 32 | 4 | 8 | 24 | 32 |
| 53331 | 66 × 66, 3 × 3, 2 × 2 | 27 | 59 | 39 | 71 |
| 72222 | 24 × 24, 2 × 2 | 6 | 8 | 24 | 26 |
| 7311111 | 50 × 50, 2 × 2 | 6 | 16 | 32 | 52 |
| 54411 | 48 × 48 | 4 | 8 | 36 | 48 |
| 55221 | 54 × 54, 2 × 2 | 6 | 16 | 38 | 56 |
| 9111111 | 32 × 32 | 2 | 4 | 24 | 32 |
| 55311 | 84 × 84, 4 × 4 | 15 | 44 | 49 | 88 |
| 73221 | 80 × 80, 4 × 4, 4 × 4 | 12 | 32 | 56 | 88 |
| 555 | 54 × 54, 2 × 2 | 4 | 6 | 38 | 56 |
| 66111 | 20 × 20 | 2 | 2 | 20 | 20 |
| 73311 | 98 × 98, 4 × 4, 4 × 4 | 12 | 38 | 58 | 106 |
| 663 | 40 × 40, 3 × 3 | 4 | 6 | 40 | 43 |
| 744 | 48 × 48, 4 × 4 | 4 | 8 | 48 | 52 |
| 75111 | 91 × 91, 4 × 4 | 6 | 18 | 58 | 95 |
| 92211 | 64 × 64 | 4 | 8 | 48 | 64 |
| 753 | 126 × 126, 8 × 8, 8 × 8 | 18 | 50 | 87 | 142 |
| 93111 | 100 × 100, 4 × 4 | 6 | 16 | 64 | 104 |
| (11,1,1,1,1) | 64 × 64 | 2 | 4 | 48 | 64 |
| 771 | 100 × 100, 5 × 5, 5 × 5 | 3 | 9 | 70 | 110 |
| 933 | 108 × 108, 4 × 4, 4 × 4 | 6 | 16 | 76 | 116 |
| (11,2,2) | 64 × 64, 4 × 4 | 4 | 6 | 64 | 68 |
| 951 | 146 × 146, 8 × 8, 1 × 1 | 4 | 17 | 102 | 155 |
| (11,3,1) | 160 × 160, 8 × 8, 8 × 8 | 6 | 18 | 112 | 176 |
| (13,1,1) | 128 × 128 | 2 | 4 | 96 | 128 |
| (15) | 128 × 128, 8 × 8 | 2 | 4 | 128 | 136 |
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.