Base field 4.4.9792.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 2x + 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ |
| 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:
| \(x^{4} - 58x^{2} + 800\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $-1$ |
| 7 | $[7, 7, w]$ | $-\frac{1}{2}e^{2} + 13$ |
| 7 | $[7, 7, w^{3} - 3w^{2} - 4w + 5]$ | $-\frac{1}{2}e^{2} + 13$ |
| 9 | $[9, 3, w^{3} - 4w^{2} - w + 9]$ | $\phantom{-}e$ |
| 17 | $[17, 17, 2w^{3} - 6w^{2} - 7w + 8]$ | $\phantom{-}\frac{3}{20}e^{3} - \frac{47}{10}e$ |
| 17 | $[17, 17, -w^{3} + 3w^{2} + 4w - 3]$ | $\phantom{-}\frac{1}{40}e^{3} - \frac{29}{20}e$ |
| 17 | $[17, 17, -w + 2]$ | $\phantom{-}\frac{1}{40}e^{3} - \frac{29}{20}e$ |
| 23 | $[23, 23, 2w^{3} - 7w^{2} - 4w + 12]$ | $\phantom{-}\frac{3}{40}e^{3} - \frac{27}{20}e$ |
| 23 | $[23, 23, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{3}{40}e^{3} - \frac{27}{20}e$ |
| 31 | $[31, 31, -2w^{3} + 7w^{2} + 5w - 12]$ | $-e^{2} + 32$ |
| 31 | $[31, 31, -w^{3} + 4w^{2} + 2w - 8]$ | $-e^{2} + 32$ |
| 41 | $[41, 41, 3w^{3} - 10w^{2} - 7w + 16]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{14}{5}e$ |
| 41 | $[41, 41, 2w^{3} - 7w^{2} - 5w + 10]$ | $\phantom{-}\frac{1}{10}e^{3} - \frac{14}{5}e$ |
| 49 | $[49, 7, 2w^{3} - 6w^{2} - 6w + 9]$ | $-e^{2} + 30$ |
| 71 | $[71, 71, w^{2} - 2w - 2]$ | $-\frac{2}{5}e^{3} + \frac{61}{5}e$ |
| 71 | $[71, 71, 2w^{3} - 7w^{2} - 4w + 13]$ | $-\frac{2}{5}e^{3} + \frac{61}{5}e$ |
| 73 | $[73, 73, 3w^{3} - 11w^{2} - 5w + 19]$ | $\phantom{-}e^{2} - 36$ |
| 73 | $[73, 73, -4w^{3} + 13w^{2} + 10w - 17]$ | $\phantom{-}e^{2} - 36$ |
| 79 | $[79, 79, 3w^{3} - 9w^{2} - 10w + 13]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -2w^{3} + 6w^{2} + 5w - 8]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{3} - 3w^{2} - 3w + 4]$ | $1$ |