Base field 4.4.13968.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 7 x^2 + 8 x + 4\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8,4,-w + 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, \frac{1}{2} w^2 + \frac{1}{2} w - 1]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -\frac{1}{2} w^2 + \frac{3}{2} w]$ | $-2$ |
| 9 | $[9, 3, -\frac{1}{2} w^2 + \frac{1}{2} w + 2]$ | $\phantom{-}1$ |
| 13 | $[13, 13, \frac{1}{2} w^3 - w^2 - \frac{5}{2} w + 2]$ | $-5$ |
| 13 | $[13, 13, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 3 w - 1]$ | $-1$ |
| 23 | $[23, 23, \frac{1}{2} w^3 - w^2 - \frac{5}{2} w]$ | $-4$ |
| 23 | $[23, 23, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 3 w - 3]$ | $-4$ |
| 37 | $[37, 37, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w - 3]$ | $\phantom{-}5$ |
| 37 | $[37, 37, \frac{1}{2} w^3 - w^2 - \frac{5}{2} w + 6]$ | $\phantom{-}1$ |
| 59 | $[59, 59, -\frac{1}{2} w^3 + \frac{7}{2} w]$ | $-8$ |
| 59 | $[59, 59, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + 2 w - 3]$ | $\phantom{-}0$ |
| 61 | $[61, 61, -w^3 + 2 w^2 + 7 w - 7]$ | $\phantom{-}15$ |
| 61 | $[61, 61, w^3 - w^2 - 6 w + 3]$ | $\phantom{-}2$ |
| 61 | $[61, 61, w^3 - 2 w^2 - 5 w + 3]$ | $\phantom{-}2$ |
| 61 | $[61, 61, w^3 - w^2 - 8 w + 1]$ | $-5$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 5 w - 5]$ | $-4$ |
| 71 | $[71, 71, -w^3 + \frac{3}{2} w^2 + \frac{15}{2} w - 6]$ | $-12$ |
| 83 | $[83, 83, -\frac{1}{2} w^3 + \frac{3}{2} w^2 + 2 w - 7]$ | $\phantom{-}0$ |
| 83 | $[83, 83, \frac{1}{2} w^3 - \frac{7}{2} w - 4]$ | $\phantom{-}0$ |
| 97 | $[97, 97, 2 w - 1]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-\frac{1}{2} w^2 - \frac{1}{2} w + 1]$ | $-1$ |