Base field 4.4.10025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 10x + 20\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w + 2]$ | $\phantom{-}1$ |
| 4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ | $-1$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ | $-e - 2$ |
| 19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w - 1]$ | $-2e - 2$ |
| 31 | $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ | $-e - 8$ |
| 31 | $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ | $\phantom{-}e + 4$ |
| 49 | $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ | $\phantom{-}2e + 2$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ | $-10$ |
| 59 | $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ | $\phantom{-}4e + 4$ |
| 59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ | $-2e + 8$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ | $-2$ |
| 61 | $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ | $\phantom{-}4e + 2$ |
| 71 | $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ | $-12$ |
| 71 | $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ | $-2$ |
| 79 | $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ | $\phantom{-}4e + 4$ |
| 79 | $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ | $\phantom{-}2e + 2$ |
| 81 | $[81, 3, -3]$ | $-e - 8$ |
| 89 | $[89, 89, w^{3} - 7w + 1]$ | $-5e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, -w + 2]$ | $-1$ |
| $4$ | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ | $1$ |