A₇ · Neutral gradings
22 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 11111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 2111111 | 2 × 2 | 2 | 2 | 2 | 2 |
| 221111 | 3 × 3 | 3 | 3 | 3 | 3 |
| 311111 | 5 × 5 | 3 | 3 | 5 | 5 |
| 22211 | 4 × 4 | 4 | 4 | 4 | 4 |
| 2222 | 5 × 5, 1 × 1 | 5 | 6 | 5 | 6 |
| 32111 | 10 × 10 | 6 | 6 | 10 | 10 |
| 41111 | 8 × 8 | 2 | 2 | 8 | 8 |
| 3221 | 15 × 15, 1 × 1 | 9 | 10 | 15 | 16 |
| 3311 | 14 × 14, 1 × 1 | 6 | 7 | 14 | 15 |
| 332 | 20 × 20 | 6 | 6 | 20 | 20 |
| 4211 | 18 × 18 | 6 | 6 | 18 | 18 |
| 422 | 28 × 28, 2 × 2 | 10 | 12 | 28 | 30 |
| 5111 | 20 × 20 | 2 | 2 | 20 | 20 |
| 431 | 40 × 40, 2 × 2 | 6 | 8 | 40 | 42 |
| 44 | 35 × 35, 3 × 3, 1 × 1, 1 × 1 | 3 | 8 | 35 | 40 |
| 521 | 40 × 40 | 4 | 4 | 40 | 40 |
| 53 | 65 × 65, 4 × 4, 1 × 1, 1 × 1 | 6 | 10 | 65 | 71 |
| 611 | 32 × 32 | 2 | 2 | 32 | 32 |
| 62 | 72 × 72, 5 × 5, 1 × 1, 1 × 1 | 4 | 6 | 72 | 79 |
| 71 | 80 × 80, 4 × 4, 1 × 1, 1 × 1 | 2 | 2 | 80 | 86 |
| 8 | 128 × 128, 8 × 8, 2 × 2, 2 × 2, 1 × 1, 1 × 1, 1 × 1, 1 × 1 | 2 | 12 | 128 | 144 |
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.