Base field 4.4.19525.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 14x^{2} + 15x + 45\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[25, 5, \frac{2}{3}w^{2} - \frac{2}{3}w - 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $46$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 9x^{3} + 18x^{2} - 19x - 40\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $-1$ |
| 5 | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $-1$ |
| 9 | $[9, 3, -w + 3]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, \frac{2}{3}w^{2} + \frac{1}{3}w - 4]$ | $-4e^{3} - 18e^{2} + 8e + 32$ |
| 16 | $[16, 2, 2]$ | $-e^{3} - 4e^{2} + 4e + 13$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - \frac{10}{3}w - 3]$ | $-2e^{3} - 10e^{2} - e + 20$ |
| 19 | $[19, 19, \frac{1}{3}w^{3} - w^{2} - \frac{7}{3}w + 6]$ | $-2e^{3} - 10e^{2} - e + 20$ |
| 29 | $[29, 29, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 2]$ | $-3e^{3} - 14e^{2} + 5e + 30$ |
| 29 | $[29, 29, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ | $-3e^{3} - 14e^{2} + 5e + 30$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w + 1]$ | $\phantom{-}5e^{3} + 22e^{2} - 11e - 38$ |
| 31 | $[31, 31, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{8}{3}w - 4]$ | $\phantom{-}5e^{3} + 22e^{2} - 11e - 38$ |
| 49 | $[49, 7, \frac{1}{3}w^{3} - \frac{10}{3}w - 1]$ | $-7e^{3} - 31e^{2} + 19e + 70$ |
| 49 | $[49, 7, -\frac{1}{3}w^{3} + w^{2} + \frac{7}{3}w - 4]$ | $-7e^{3} - 31e^{2} + 19e + 70$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{5}{3}w - 11]$ | $\phantom{-}11e^{3} + 49e^{2} - 24e - 90$ |
| 59 | $[59, 59, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 5w - 13]$ | $\phantom{-}11e^{3} + 49e^{2} - 24e - 90$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{2}{3}w - 9]$ | $\phantom{-}8e^{3} + 37e^{2} - 16e - 82$ |
| 61 | $[61, 61, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 4w + 2]$ | $\phantom{-}2e^{2} + 7e - 2$ |
| 61 | $[61, 61, \frac{2}{3}w^{2} - \frac{5}{3}w - 1]$ | $\phantom{-}2e^{2} + 7e - 2$ |
| 61 | $[61, 61, -\frac{1}{3}w^{2} + \frac{4}{3}w + 6]$ | $\phantom{-}8e^{3} + 37e^{2} - 16e - 82$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, \frac{2}{3}w^{2} + \frac{1}{3}w - 5]$ | $1$ |
| $5$ | $[5, 5, \frac{2}{3}w^{2} - \frac{5}{3}w - 4]$ | $1$ |