Base field 4.4.8525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 8x^{2} + 9x + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, 2w^{2} - 2w - 9]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 6x^{3} + x^{2} + 18x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 2]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $-2e + 4$ |
| 11 | $[11, 11, w^{2} - 5]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}e^{2} - 4e + 1$ |
| 19 | $[19, 19, -w]$ | $-e^{3} + 6e^{2} - 3e - 8$ |
| 19 | $[19, 19, -w + 1]$ | $-e^{3} + 6e^{2} - 3e - 8$ |
| 31 | $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}e^{3} - 7e^{2} + 7e + 12$ |
| 31 | $[31, 31, -w^{2} + 2w + 7]$ | $\phantom{-}2e - 8$ |
| 31 | $[31, 31, -w^{3} + 5w + 5]$ | $\phantom{-}e^{3} - 7e^{2} + 7e + 12$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}e^{3} - 8e^{2} + 10e + 18$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}e^{3} - 8e^{2} + 10e + 18$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}2e^{2} - 8e - 4$ |
| 59 | $[59, 59, -w^{3} + w^{2} + 4w + 5]$ | $-2e^{3} + 12e^{2} - 8e - 20$ |
| 59 | $[59, 59, w^{3} - 5w^{2} - w + 18]$ | $-2e^{3} + 12e^{2} - 8e - 20$ |
| 59 | $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ | $\phantom{-}2e^{2} - 8e - 4$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}e^{3} - 4e^{2} - 6e + 10$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} - 3]$ | $\phantom{-}e^{3} - 6e^{2} + 7e + 6$ |
| 89 | $[89, 89, -4w^{2} + 5w + 20]$ | $\phantom{-}e^{3} - 6e^{2} + 7e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w + 1]$ | $-1$ |
| $5$ | $[5, 5, -w + 2]$ | $-1$ |