Base field \(\Q(\sqrt{6}) \)
Generator \(w\), with minimal polynomial \(x^2 - 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[25, 5, 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 - x^3 - 8 x^2 + 4 x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 3]$ | $-e^2 + e + 4$ |
| 5 | $[5, 5, w + 1]$ | $-1$ |
| 5 | $[5, 5, w - 1]$ | $-1$ |
| 19 | $[19, 19, w + 5]$ | $\phantom{-}e^3 - e^2 - 6 e + 2$ |
| 19 | $[19, 19, -w + 5]$ | $\phantom{-}e^3 - e^2 - 6 e + 2$ |
| 23 | $[23, 23, -2 w + 1]$ | $\phantom{-}e^3 - 2 e^2 - 5 e + 6$ |
| 23 | $[23, 23, -2 w - 1]$ | $\phantom{-}e^3 - 2 e^2 - 5 e + 6$ |
| 29 | $[29, 29, -3 w + 5]$ | $-e^3 - e^2 + 6 e + 6$ |
| 29 | $[29, 29, -3 w - 5]$ | $-e^3 - e^2 + 6 e + 6$ |
| 43 | $[43, 43, -w - 7]$ | $\phantom{-}e^2 - e - 4$ |
| 43 | $[43, 43, w - 7]$ | $\phantom{-}e^2 - e - 4$ |
| 47 | $[47, 47, 4 w - 7]$ | $-e^3 + 3 e + 6$ |
| 47 | $[47, 47, 6 w - 13]$ | $-e^3 + 3 e + 6$ |
| 49 | $[49, 7, -7]$ | $-e^3 + e^2 + 8 e + 2$ |
| 53 | $[53, 53, -3 w - 1]$ | $\phantom{-}2 e^2 - 2 e - 6$ |
| 53 | $[53, 53, 3 w - 1]$ | $\phantom{-}2 e^2 - 2 e - 6$ |
| 67 | $[67, 67, -7 w + 19]$ | $-2 e^3 + e^2 + 9 e - 4$ |
| 67 | $[67, 67, -3 w + 11]$ | $-2 e^3 + e^2 + 9 e - 4$ |
| 71 | $[71, 71, -4 w - 5]$ | $\phantom{-}2 e^2 + 2 e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 1]$ | $1$ |
| $5$ | $[5, 5, w - 1]$ | $1$ |