Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 7 x^2 + 2 x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[4, 2, w^3 - 3 w^2 - 3 w + 4]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^4 - 58 x^2 + 800\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^3 - 3 w^2 - 3 w + 4]$ | $-1$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{2} e^2 + 13$ |
| 7 | $[7, 7, w^3 - 3 w^2 - 4 w + 5]$ | $-\frac{1}{2} e^2 + 13$ |
| 9 | $[9, 3, w^3 - 4 w^2 - w + 9]$ | $\phantom{-}e$ |
| 17 | $[17, 17, 2 w^3 - 6 w^2 - 7 w + 8]$ | $\phantom{-}\frac{3}{20} e^3 - \frac{47}{10} e$ |
| 17 | $[17, 17, -w^3 + 3 w^2 + 4 w - 3]$ | $\phantom{-}\frac{1}{40} e^3 - \frac{29}{20} e$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{1}{40} e^3 - \frac{29}{20} e$ |
| 23 | $[23, 23, 2 w^3 - 7 w^2 - 4 w + 12]$ | $\phantom{-}\frac{3}{40} e^3 - \frac{27}{20} e$ |
| 23 | $[23, 23, -w^2 + 2 w + 3]$ | $\phantom{-}\frac{3}{40} e^3 - \frac{27}{20} e$ |
| 31 | $[31, 31, -2 w^3 + 7 w^2 + 5 w - 12]$ | $-e^2 + 32$ |
| 31 | $[31, 31, -w^3 + 4 w^2 + 2 w - 8]$ | $-e^2 + 32$ |
| 41 | $[41, 41, 3 w^3 - 10 w^2 - 7 w + 16]$ | $\phantom{-}\frac{1}{10} e^3 - \frac{14}{5} e$ |
| 41 | $[41, 41, 2 w^3 - 7 w^2 - 5 w + 10]$ | $\phantom{-}\frac{1}{10} e^3 - \frac{14}{5} e$ |
| 49 | $[49, 7, 2 w^3 - 6 w^2 - 6 w + 9]$ | $-e^2 + 30$ |
| 71 | $[71, 71, w^2 - 2 w - 2]$ | $-\frac{2}{5} e^3 + \frac{61}{5} e$ |
| 71 | $[71, 71, 2 w^3 - 7 w^2 - 4 w + 13]$ | $-\frac{2}{5} e^3 + \frac{61}{5} e$ |
| 73 | $[73, 73, 3 w^3 - 11 w^2 - 5 w + 19]$ | $\phantom{-}e^2 - 36$ |
| 73 | $[73, 73, -4 w^3 + 13 w^2 + 10 w - 17]$ | $\phantom{-}e^2 - 36$ |
| 79 | $[79, 79, 3 w^3 - 9 w^2 - 10 w + 13]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -2 w^3 + 6 w^2 + 5 w - 8]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^3 - 3 w^2 - 3 w + 4]$ | $1$ |