E₆ · Neutral gradings
21 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 1 | 1 × 1 | 1 | 1 | 1 | 1 |
| A₁ | 2 × 2 | 2 | 2 | 2 | 2 |
| 2A₁ | 3 × 3 | 3 | 3 | 3 | 3 |
| 3A₁ | 4 × 4 | 4 | 4 | 4 | 4 |
| A₂ | 6 × 6 | 5 | 6 | 5 | 6 |
| A₂ + A₁ | 10 × 10 | 6 | 6 | 10 | 10 |
| 2A₂ | 10 × 10, 1 × 1, 1 × 1 | 3 | 5 | 10 | 12 |
| A₂ + 2A₁ | 10 × 10 | 7 | 8 | 9 | 10 |
| A₃ | 6 × 6 | 2 | 2 | 6 | 6 |
| 2A₂ + A₁ | 20 × 20, 2 × 2, 2 × 2 | 6 | 10 | 20 | 24 |
| A₃ + A₁ | 18 × 18, 1 × 1, 1 × 1 | 6 | 8 | 18 | 20 |
| D₄(a₁) | 21 × 21, 2 × 2, 2 × 2 | 11 | 18 | 18 | 25 |
| D₄ | 8 × 8 | 2 | 2 | 8 | 8 |
| A₄ | 23 × 23, 1 × 1, 1 × 1 | 3 | 3 | 23 | 25 |
| A₄ + A₁ | 40 × 40, 2 × 2, 2 × 2 | 4 | 4 | 40 | 44 |
| A₅ | 32 × 32, 2 × 2, 2 × 2 | 2 | 6 | 32 | 36 |
| D₅(a₁) | 30 × 30 | 4 | 4 | 30 | 30 |
| E₆(a₃) | 53 × 53, 4 × 4, 4 × 4, 1 × 1, 1 × 1 | 6 | 18 | 49 | 63 |
| D₅ | 36 × 36, 2 × 2, 2 × 2 | 2 | 2 | 36 | 40 |
| E₆(a₁) | 60 × 60, 4 × 4, 4 × 4 | 2 | 6 | 60 | 68 |
| E₆ | 64 × 64, 4 × 4, 4 × 4 | 2 | 6 | 64 | 72 |
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.