Base field \(\Q(\sqrt{2}, \sqrt{5})\)
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[89,89,\frac{1}{2}w^{3} - w^{2} - 3w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 6x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 2w]$ | $\phantom{-}2$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 3]$ | $\phantom{-}0$ |
| 25 | $[25, 5, w^{2} - 3]$ | $\phantom{-}2e - 10$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w]$ | $\phantom{-}4$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} - w + 3]$ | $-2e + 4$ |
| 31 | $[31, 31, -\frac{1}{2}w^{2} + w + 3]$ | $-3e + 12$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w]$ | $\phantom{-}2e - 8$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - w^{2} - w + 3]$ | $\phantom{-}4e - 12$ |
| 41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $-4e + 12$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - w + 5]$ | $-3e + 12$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - w^{2} + w + 3]$ | $-2e + 12$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + 2w - 3]$ | $\phantom{-}3e - 12$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - 2w - 3]$ | $-2e + 4$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 2w - 5]$ | $-5e + 12$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 5]$ | $-2e - 4$ |
| 71 | $[71, 71, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 5]$ | $\phantom{-}2e - 12$ |
| 71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 2w - 5]$ | $\phantom{-}e - 4$ |
| 79 | $[79, 79, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 2w - 4]$ | $-6e + 20$ |
| 79 | $[79, 79, -w^{3} - \frac{1}{2}w^{2} + 6w]$ | $-6e + 20$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $89$ | $[89,89,\frac{1}{2}w^{3} - w^{2} - 3w + 1]$ | $1$ |