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: | $2$ |
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:
\(x^{2} - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $-1$ |
5 | $[5, 5, -w + 2]$ | $-1$ |
11 | $[11, 11, w^{2} - 2w - 4]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{2} + 3]$ | $-e$ |
11 | $[11, 11, w^{2} - 5]$ | $\phantom{-}e$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{3}{2}e + 2$ |
19 | $[19, 19, -w]$ | $\phantom{-}2$ |
19 | $[19, 19, -w + 1]$ | $\phantom{-}2$ |
31 | $[31, 31, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}e + 2$ |
31 | $[31, 31, -w^{2} + 2w + 7]$ | $-10$ |
31 | $[31, 31, -w^{3} + 5w + 5]$ | $\phantom{-}e + 2$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}2e$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $\phantom{-}2e$ |
59 | $[59, 59, -w^{3} + w^{2} + 6w - 2]$ | $-6$ |
59 | $[59, 59, -w^{3} + w^{2} + 4w + 5]$ | $\phantom{-}e + 6$ |
59 | $[59, 59, w^{3} - 5w^{2} - w + 18]$ | $\phantom{-}e + 6$ |
59 | $[59, 59, w^{3} - 2w^{2} - 5w + 4]$ | $-6$ |
81 | $[81, 3, -3]$ | $\phantom{-}16$ |
89 | $[89, 89, -w^{3} + 3w^{2} - 3]$ | $-3e + 6$ |
89 | $[89, 89, -4w^{2} + 5w + 20]$ | $-3e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 1]$ | $1$ |
$5$ | $[5, 5, -w + 2]$ | $1$ |