Base field 4.4.6125.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 9x + 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, -2w^{3} - 2w^{2} + 12w + 7]$ |
| Dimension: | $2$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 4x - 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ | $\phantom{-}0$ |
| 11 | $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} + w^{2} - 7w - 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
| 16 | $[16, 2, 2]$ | $-\frac{3}{2}e - \frac{5}{2}$ |
| 19 | $[19, 19, -w^{2} + 4]$ | $\phantom{-}0$ |
| 19 | $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ | $\phantom{-}0$ |
| 19 | $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w^{3} - w^{2} + 5w + 3]$ | $\phantom{-}0$ |
| 49 | $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ | $\phantom{-}0$ |
| 59 | $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ | $\phantom{-}0$ |
| 59 | $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ | $\phantom{-}e + 10$ |
| 71 | $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ | $\phantom{-}e + 10$ |
| 71 | $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ | $\phantom{-}e + 10$ |
| 71 | $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ | $\phantom{-}e + 10$ |
| 81 | $[81, 3, -3]$ | $-18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ | $1$ |