C₄ · Neutral gradings
14 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, 1 × 1 | 2 | 3 | 2 | 3 |
| 221111 | 4 × 4, 1 × 1 | 3 | 5 | 3 | 5 |
| 22211 | 5 × 5, 2 × 2 | 4 | 7 | 4 | 7 |
| 2222 | 7 × 7, 2 × 2 | 5 | 9 | 5 | 9 |
| 41111 | 4 × 4, 2 × 2 | 2 | 4 | 4 | 6 |
| 3311 | 4 × 4 | 3 | 3 | 4 | 4 |
| 4211 | 10 × 10, 4 × 4, 1 × 1 | 6 | 13 | 8 | 15 |
| 332 | 6 × 6, 3 × 3 | 4 | 6 | 6 | 9 |
| 422 | 16 × 16, 8 × 8, 1 × 1 | 10 | 23 | 12 | 25 |
| 44 | 14 × 14, 5 × 5, 1 × 1 | 3 | 8 | 11 | 20 |
| 611 | 8 × 8, 4 × 4 | 2 | 4 | 8 | 12 |
| 62 | 20 × 20, 8 × 8, 2 × 2 | 4 | 12 | 16 | 30 |
| 8 | 16 × 16, 8 × 8 | 2 | 4 | 16 | 24 |
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.