Base field 4.4.8000.1
Generator \(w\), with minimal polynomial \(x^4 - 10 x^2 + 20\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -w^2 + 5]$ |
| Dimension: | $1$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2} w^3 - 3 w + 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w^2 - w - 5]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + 3 w + 3]$ | $-6$ |
| 11 | $[11, 11, -\frac{1}{2} w^2 + w + 2]$ | $-6$ |
| 11 | $[11, 11, -\frac{1}{2} w^2 - w + 2]$ | $-6$ |
| 11 | $[11, 11, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w + 3]$ | $-6$ |
| 29 | $[29, 29, -\frac{1}{2} w^2 - w + 4]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2} w^3 + \frac{1}{2} w^2 + 3 w - 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2} w^3 - \frac{1}{2} w^2 + 3 w + 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, -\frac{1}{2} w^2 + w + 4]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w^3 - \frac{1}{2} w^2 - 6 w + 6]$ | $-6$ |
| 41 | $[41, 41, -\frac{1}{2} w^3 + \frac{5}{2} w^2 + 5 w - 14]$ | $-6$ |
| 41 | $[41, 41, \frac{1}{2} w^3 - \frac{1}{2} w^2 - 3 w + 6]$ | $-6$ |
| 41 | $[41, 41, -\frac{3}{2} w^2 - 2 w + 6]$ | $-6$ |
| 79 | $[79, 79, -w^3 - w^2 + 4 w - 1]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -\frac{3}{2} w^2 - w + 9]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -w^3 + \frac{7}{2} w^2 + 9 w - 21]$ | $\phantom{-}0$ |
| 79 | $[79, 79, w^3 - w^2 - 6 w + 9]$ | $\phantom{-}0$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}14$ |
| 109 | $[109, 109, w^2 - w - 7]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, w^2 - w - 5]$ | $1$ |