D₆ · Neutral gradings
31 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 111111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 2211111111 | 2 × 2 | 2 | 2 | 2 | 2 |
| 3111111111 | 3 × 3, 1 × 1 | 3 | 4 | 3 | 4 |
| 22221111 | 3 × 3 | 3 | 3 | 3 | 3 |
| 222222+ | 4 × 4, 1 × 1 | 4 | 5 | 4 | 5 |
| 222222- | 4 × 4, 1 × 1 | 4 | 5 | 4 | 5 |
| 32211111 | 6 × 6, 2 × 2 | 6 | 8 | 6 | 8 |
| 33111111 | 7 × 7, 2 × 2 | 6 | 9 | 6 | 9 |
| 322221 | 12 × 12, 3 × 3, 2 × 2, 2 × 2 | 12 | 19 | 12 | 19 |
| 51111111 | 6 × 6, 2 × 2 | 2 | 4 | 6 | 8 |
| 332211 | 16 × 16, 4 × 4, 2 × 2, 2 × 2 | 14 | 24 | 14 | 24 |
| 333111 | 13 × 13, 4 × 4, 2 × 2, 2 × 2 | 11 | 21 | 11 | 21 |
| 3333 | 11 × 11, 3 × 3 | 5 | 8 | 10 | 14 |
| 441111 | 6 × 6 | 2 | 2 | 6 | 6 |
| 522111 | 12 × 12, 4 × 4 | 4 | 8 | 12 | 16 |
| 4422+ | 13 × 13, 2 × 2 | 6 | 8 | 13 | 15 |
| 4422- | 13 × 13, 2 × 2 | 6 | 8 | 13 | 15 |
| 531111 | 18 × 18, 8 × 8 | 9 | 19 | 16 | 26 |
| 4431 | 24 × 24, 6 × 6, 4 × 4, 4 × 4 | 8 | 18 | 24 | 38 |
| 5322 | 30 × 30, 8 × 8, 4 × 4, 4 × 4 | 16 | 32 | 30 | 46 |
| 711111 | 12 × 12, 4 × 4 | 2 | 4 | 12 | 16 |
| 5331 | 34 × 34, 14 × 14, 5 × 5, 5 × 5 | 20 | 48 | 30 | 58 |
| 5511 | 28 × 28, 10 × 10 | 3 | 8 | 25 | 38 |
| 7221 | 32 × 32, 8 × 8, 4 × 4, 4 × 4 | 4 | 12 | 32 | 48 |
| 66+ | 20 × 20, 3 × 3 | 2 | 4 | 20 | 23 |
| 66- | 20 × 20, 3 × 3 | 2 | 4 | 20 | 23 |
| 7311 | 40 × 40, 16 × 16, 5 × 5, 5 × 5 | 6 | 20 | 36 | 66 |
| 75 | 55 × 55, 15 × 15, 8 × 8, 8 × 8 | 8 | 24 | 55 | 86 |
| 9111 | 24 × 24, 8 × 8 | 2 | 4 | 24 | 32 |
| 93 | 60 × 60, 16 × 16, 8 × 8, 8 × 8 | 4 | 12 | 60 | 92 |
| (11,1) | 64 × 64, 16 × 16, 8 × 8, 8 × 8 | 2 | 8 | 64 | 96 |
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.