D₇ · Neutral gradings
43 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 11111111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 221111111111 | 2 × 2 | 2 | 2 | 2 | 2 |
| 311111111111 | 3 × 3, 1 × 1 | 3 | 4 | 3 | 4 |
| 2222111111 | 3 × 3 | 3 | 3 | 3 | 3 |
| 3221111111 | 6 × 6, 2 × 2 | 6 | 8 | 6 | 8 |
| 22222211 | 4 × 4 | 4 | 4 | 4 | 4 |
| 3311111111 | 7 × 7, 2 × 2 | 6 | 9 | 6 | 9 |
| 5111111111 | 6 × 6, 2 × 2 | 2 | 4 | 6 | 8 |
| 32222111 | 9 × 9, 3 × 3 | 9 | 12 | 9 | 12 |
| 33221111 | 14 × 14, 4 × 4 | 12 | 18 | 12 | 18 |
| 332222 | 15 × 15, 3 × 3 | 9 | 12 | 15 | 18 |
| 33311111 | 12 × 12, 4 × 4 | 10 | 16 | 10 | 16 |
| 44111111 | 6 × 6 | 2 | 2 | 6 | 6 |
| 52211111 | 12 × 12, 4 × 4 | 4 | 8 | 12 | 16 |
| 333221 | 20 × 20, 6 × 6 | 14 | 22 | 18 | 26 |
| 53111111 | 18 × 18, 8 × 8 | 9 | 19 | 16 | 26 |
| 333311 | 17 × 17, 5 × 5 | 12 | 20 | 14 | 22 |
| 522221 | 24 × 24, 6 × 6, 1 × 1, 1 × 1 | 6 | 14 | 24 | 32 |
| 71111111 | 12 × 12, 4 × 4 | 2 | 4 | 12 | 16 |
| 442211 | 13 × 13 | 6 | 6 | 13 | 13 |
| 443111 | 18 × 18, 6 × 6 | 6 | 8 | 18 | 24 |
| 532211 | 40 × 40, 16 × 16, 1 × 1, 1 × 1 | 18 | 40 | 36 | 58 |
| 4433 | 30 × 30, 6 × 6 | 6 | 8 | 30 | 36 |
| 533111 | 40 × 40, 18 × 18, 1 × 1, 1 × 1 | 21 | 48 | 33 | 60 |
| 5333 | 39 × 39, 16 × 16 | 14 | 30 | 35 | 55 |
| 551111 | 25 × 25, 10 × 10 | 3 | 8 | 22 | 35 |
| 722111 | 24 × 24, 8 × 8 | 4 | 8 | 24 | 32 |
| 5441 | 48 × 48, 12 × 12, 2 × 2, 2 × 2 | 4 | 12 | 48 | 64 |
| 5522 | 40 × 40, 10 × 10, 1 × 1, 1 × 1 | 6 | 10 | 40 | 52 |
| 731111 | 36 × 36, 16 × 16 | 6 | 16 | 32 | 52 |
| 5531 | 58 × 58, 25 × 25, 2 × 2, 2 × 2 | 15 | 41 | 51 | 87 |
| 7322 | 60 × 60, 16 × 16, 1 × 1, 1 × 1 | 8 | 18 | 60 | 78 |
| 911111 | 24 × 24, 8 × 8 | 2 | 4 | 24 | 32 |
| 6611 | 20 × 20 | 2 | 2 | 20 | 20 |
| 7331 | 68 × 68, 28 × 28, 1 × 1, 1 × 1 | 10 | 30 | 60 | 98 |
| 7511 | 72 × 72, 30 × 30, 2 × 2, 2 × 2 | 6 | 18 | 65 | 106 |
| 9221 | 64 × 64, 16 × 16, 2 × 2, 2 × 2 | 4 | 12 | 64 | 84 |
| 77 | 75 × 75, 20 × 20, 1 × 1, 1 × 1 | 3 | 6 | 75 | 97 |
| 9311 | 80 × 80, 32 × 32, 2 × 2, 2 × 2 | 6 | 20 | 72 | 116 |
| (11,1,1,1) | 48 × 48, 16 × 16 | 2 | 4 | 48 | 64 |
| 95 | 110 × 110, 30 × 30, 4 × 4, 4 × 4 | 4 | 16 | 110 | 148 |
| (11,3) | 120 × 120, 32 × 32, 2 × 2, 2 × 2 | 4 | 12 | 120 | 156 |
| (13,1) | 128 × 128, 32 × 32, 4 × 4, 4 × 4 | 2 | 8 | 128 | 168 |
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.