Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^4 - x^3 - 7 x^2 + x + 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 2, w^3 - 3 w^2 - 3 w + 9]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^2 + 2]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w^3 + 2 w^2 + 4 w - 5]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w^3 + 2 w^2 + 3 w - 1]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w^3 - 2 w^2 - 3 w + 5]$ | $\phantom{-}4$ |
| 17 | $[17, 17, -w^2 - w + 3]$ | $-8$ |
| 19 | $[19, 19, -w^3 + 3 w^2 + 2 w - 7]$ | $-4$ |
| 23 | $[23, 23, w^3 - 2 w^2 - 3 w + 3]$ | $-8$ |
| 31 | $[31, 31, -w^2 + w + 1]$ | $\phantom{-}4$ |
| 47 | $[47, 47, -w^3 + w^2 + 4 w - 3]$ | $-12$ |
| 49 | $[49, 7, 2 w^3 - 5 w^2 - 7 w + 11]$ | $-4$ |
| 53 | $[53, 53, -3 w^3 + 9 w^2 + 10 w - 31]$ | $\phantom{-}6$ |
| 53 | $[53, 53, w^3 - w^2 - 4 w + 1]$ | $-6$ |
| 61 | $[61, 61, 3 w^3 - 6 w^2 - 13 w + 13]$ | $\phantom{-}8$ |
| 61 | $[61, 61, 2 w^2 - 7]$ | $-12$ |
| 71 | $[71, 71, w^2 - 3 w - 5]$ | $\phantom{-}8$ |
| 73 | $[73, 73, 2 w - 3]$ | $\phantom{-}8$ |
| 73 | $[73, 73, -2 w^3 + 6 w^2 + 6 w - 19]$ | $\phantom{-}8$ |
| 79 | $[79, 79, 2 w^2 - 5]$ | $\phantom{-}0$ |
| 81 | $[81, 3, -3]$ | $-2$ |
| 101 | $[101, 101, 2 w^2 - 4 w - 9]$ | $\phantom{-}12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w^3 + 2 w^2 + 4 w - 5]$ | $1$ |