Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^{2} + 5]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - 3w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - w - 5]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 3]$ | $\phantom{-}e + 2$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $-e + 2$ |
| 11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $-e + 2$ |
| 11 | $[11, 11, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 3]$ | $\phantom{-}e + 2$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} - w + 4]$ | $-e - 6$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $-e + 6$ |
| 29 | $[29, 29, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 3w + 1]$ | $-e + 6$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} + w + 4]$ | $-e - 6$ |
| 41 | $[41, 41, w^{3} - \frac{1}{2}w^{2} - 6w + 6]$ | $\phantom{-}e + 2$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 5w - 14]$ | $-e + 2$ |
| 41 | $[41, 41, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w + 6]$ | $-e + 2$ |
| 41 | $[41, 41, -\frac{3}{2}w^{2} - 2w + 6]$ | $\phantom{-}e + 2$ |
| 79 | $[79, 79, -w^{3} - w^{2} + 4w - 1]$ | $-2e$ |
| 79 | $[79, 79, -\frac{3}{2}w^{2} - w + 9]$ | $-2e$ |
| 79 | $[79, 79, -w^{3} + \frac{7}{2}w^{2} + 9w - 21]$ | $-2e$ |
| 79 | $[79, 79, w^{3} - w^{2} - 6w + 9]$ | $-2e$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}18$ |
| 109 | $[109, 109, w^{2} - w - 7]$ | $-2e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^{2} - w - 5]$ | $1$ |