Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Generator \(w\), with minimal polynomial \(x^4 - 6 x^2 + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[89,89,w^2 - w - 5]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2} w^3 - 2 w]$ | $-2$ |
| 9 | $[9, 3, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 2 w - 3]$ | $\phantom{-}0$ |
| 9 | $[9, 3, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 2 w - 3]$ | $\phantom{-}4$ |
| 25 | $[25, 5, w^2 - 3]$ | $\phantom{-}6$ |
| 31 | $[31, 31, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 3 w]$ | $-4$ |
| 31 | $[31, 31, -\frac{1}{2} w^2 - w + 3]$ | $\phantom{-}4$ |
| 31 | $[31, 31, -\frac{1}{2} w^2 + w + 3]$ | $\phantom{-}4$ |
| 31 | $[31, 31, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w]$ | $-8$ |
| 41 | $[41, 41, \frac{1}{2} w^3 - w^2 - w + 3]$ | $\phantom{-}4$ |
| 41 | $[41, 41, w^3 + w^2 - 5 w - 3]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -\frac{3}{2} w^2 - w + 5]$ | $-8$ |
| 41 | $[41, 41, -\frac{1}{2} w^3 - w^2 + w + 3]$ | $\phantom{-}8$ |
| 49 | $[49, 7, -\frac{1}{2} w^3 + 2 w - 3]$ | $\phantom{-}8$ |
| 49 | $[49, 7, \frac{1}{2} w^3 - 2 w - 3]$ | $\phantom{-}4$ |
| 71 | $[71, 71, \frac{1}{2} w^3 + \frac{1}{2} w^2 - 2 w - 5]$ | $-4$ |
| 71 | $[71, 71, \frac{1}{2} w^3 + \frac{3}{2} w^2 - 3 w - 5]$ | $-8$ |
| 71 | $[71, 71, \frac{1}{2} w^3 - \frac{3}{2} w^2 - 3 w + 5]$ | $\phantom{-}0$ |
| 71 | $[71, 71, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 2 w - 5]$ | $\phantom{-}12$ |
| 79 | $[79, 79, \frac{1}{2} w^3 + \frac{3}{2} w^2 - 2 w - 4]$ | $-12$ |
| 79 | $[79, 79, -w^3 - \frac{1}{2} w^2 + 6 w]$ | $\phantom{-}4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $89$ | $[89,89,w^2 - w - 5]$ | $1$ |