Base field 4.4.13068.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 2, w^{3} - 2w^{2} - 4w + 3]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}0$ |
| 4 | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 6w - 1]$ | $\phantom{-}6$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}6$ |
| 29 | $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}6$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 4w]$ | $\phantom{-}6$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}8$ |
| 31 | $[31, 31, -w^{3} + 7w + 5]$ | $\phantom{-}8$ |
| 41 | $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ | $-6$ |
| 41 | $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ | $-6$ |
| 67 | $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ | $-4$ |
| 67 | $[67, 67, -w^{2} + 4w + 2]$ | $-4$ |
| 83 | $[83, 83, 2w^{2} - 5w - 2]$ | $-12$ |
| 83 | $[83, 83, -w^{3} + 8w + 6]$ | $\phantom{-}12$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ | $-12$ |
| 83 | $[83, 83, w^{3} - 2w^{2} - 6w]$ | $\phantom{-}12$ |
| 97 | $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ | $-10$ |
| 97 | $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ | $-10$ |
| 97 | $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ | $-10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w^{3} - w^{2} - 6w - 2]$ | $-1$ |
| $4$ | $[4, 2, w^{3} - w^{2} - 5w - 2]$ | $-1$ |