Base field 4.4.7600.1
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, 2w^{2} - 9]$ |
| 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:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{2}e$ |
| 9 | $[9, 3, w^{2} - w - 4]$ | $\phantom{-}\frac{1}{2}e$ |
| 11 | $[11, 11, w + 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w]$ | $\phantom{-}3e$ |
| 19 | $[19, 19, -w^{2} - w + 6]$ | $-4$ |
| 19 | $[19, 19, -w^{2} + w + 6]$ | $-4$ |
| 25 | $[25, 5, 2w^{2} - 9]$ | $-1$ |
| 29 | $[29, 29, -w^{3} + 4w + 2]$ | $-4$ |
| 29 | $[29, 29, -w^{3} + 4w - 2]$ | $-4$ |
| 41 | $[41, 41, 2w^{2} - w - 7]$ | $\phantom{-}\frac{5}{2}e$ |
| 41 | $[41, 41, w^{3} - w^{2} - 6w + 4]$ | $\phantom{-}\frac{5}{2}e$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 6w - 14]$ | $\phantom{-}\frac{1}{2}e$ |
| 61 | $[61, 61, w^{3} + 2w^{2} - 5w - 8]$ | $-\frac{1}{2}e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 5w - 8]$ | $-\frac{1}{2}e$ |
| 61 | $[61, 61, w^{3} + 3w^{2} - 6w - 14]$ | $\phantom{-}\frac{1}{2}e$ |
| 89 | $[89, 89, -w^{3} + w^{2} + 6w - 9]$ | $-12$ |
| 89 | $[89, 89, 2w^{3} - w^{2} - 10w + 10]$ | $-12$ |
| 109 | $[109, 109, -w^{3} + 5w^{2} + 7w - 23]$ | $-\frac{5}{2}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $25$ | $[25, 5, 2w^{2} - 9]$ | $1$ |