Base field 4.4.17600.1
Generator \(w\), with minimal polynomial \(x^{4} - 14x^{2} + 44\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[25, 5, \frac{1}{2}w^{2} - 1]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $52$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 20\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ | $\phantom{-}0$ |
11 | $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ | $-2$ |
11 | $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}0$ |
11 | $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ | $\phantom{-}0$ |
19 | $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ | $\phantom{-}0$ |
19 | $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ | $\phantom{-}0$ |
19 | $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ | $\phantom{-}0$ |
19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ | $\phantom{-}0$ |
25 | $[25, 5, \frac{1}{2}w^{2} - 1]$ | $\phantom{-}1$ |
29 | $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ | $-e$ |
29 | $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ | $\phantom{-}e$ |
31 | $[31, 31, -w - 1]$ | $\phantom{-}2e$ |
31 | $[31, 31, w - 1]$ | $-2e$ |
41 | $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ | $\phantom{-}2e$ |
41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ | $-2e$ |
49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ | $-e$ |
49 | $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ | $\phantom{-}e$ |
59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ | $\phantom{-}0$ |
59 | $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ | $\phantom{-}0$ |
61 | $[61, 61, \frac{1}{2}w^{2} + w - 6]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, \frac{1}{2}w^{2} - 1]$ | $-1$ |