Base field 4.4.7625.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 4x + 16\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11,11,-w + 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 13\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - \frac{3}{2}w + 4]$ | $\phantom{-}e$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 5]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -\frac{1}{4}w^{3} - \frac{3}{4}w^{2} + \frac{5}{4}w + 3]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -\frac{1}{4}w^{3} + \frac{1}{4}w^{2} + \frac{9}{4}w]$ | $\phantom{-}1$ |
| 11 | $[11, 11, w - 1]$ | $-1$ |
| 29 | $[29, 29, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{1}{4}w + 2]$ | $\phantom{-}2e$ |
| 29 | $[29, 29, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w + 3]$ | $-e$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} - \frac{1}{4}w^{2} + \frac{19}{4}w + 4]$ | $-4$ |
| 31 | $[31, 31, -\frac{3}{4}w^{3} + \frac{7}{4}w^{2} + \frac{11}{4}w - 5]$ | $\phantom{-}9$ |
| 49 | $[49, 7, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 5]$ | $-3e$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ | $-e$ |
| 59 | $[59, 59, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{5}{4}w - 3]$ | $-e$ |
| 59 | $[59, 59, w^{2} - 7]$ | $-2e$ |
| 61 | $[61, 61, -\frac{5}{4}w^{3} - \frac{7}{4}w^{2} + \frac{37}{4}w + 15]$ | $\phantom{-}6$ |
| 71 | $[71, 71, \frac{3}{4}w^{3} + \frac{9}{4}w^{2} - \frac{11}{4}w - 7]$ | $\phantom{-}12$ |
| 71 | $[71, 71, \frac{1}{4}w^{3} - \frac{1}{4}w^{2} - \frac{13}{4}w - 2]$ | $-1$ |
| 79 | $[79, 79, -\frac{1}{4}w^{3} + \frac{5}{4}w^{2} + \frac{1}{4}w - 7]$ | $\phantom{-}e$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} + \frac{3}{4}w^{2} - \frac{9}{4}w - 2]$ | $-4e$ |
| 81 | $[81, 3, -3]$ | $-4$ |
| 89 | $[89, 89, -w^{2} + 2w + 1]$ | $-5e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11,11,-w + 1]$ | $1$ |