Base field \(\Q(\sqrt{5}, \sqrt{13})\)
Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[16, 2, 2]$ |
| Dimension: | $2$ |
| 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:
| \(x^{2} - 5x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w]$ | $\phantom{-}1$ |
| 4 | $[4, 2, -\frac{1}{2}w^{3} + \frac{9}{2}w]$ | $\phantom{-}1$ |
| 9 | $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w - \frac{1}{2}]$ | $\phantom{-}e$ |
| 9 | $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w + \frac{1}{2}]$ | $\phantom{-}e$ |
| 25 | $[25, 5, \frac{1}{2}w^{3} - \frac{7}{2}w]$ | $-3e + 8$ |
| 29 | $[29, 29, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w - \frac{1}{2}]$ | $-2e + 2$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ | $-2e + 2$ |
| 29 | $[29, 29, -\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ | $-2e + 2$ |
| 29 | $[29, 29, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ | $-2e + 2$ |
| 49 | $[49, 7, \frac{3}{4}w^{3} + \frac{1}{2}w^{2} - \frac{23}{4}w - \frac{3}{2}]$ | $\phantom{-}e - 8$ |
| 49 | $[49, 7, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ | $\phantom{-}e - 8$ |
| 61 | $[61, 61, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 1]$ | $\phantom{-}2e - 6$ |
| 61 | $[61, 61, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{13}{4}w + \frac{7}{2}]$ | $\phantom{-}2e - 6$ |
| 61 | $[61, 61, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{13}{4}w - \frac{7}{2}]$ | $\phantom{-}2e - 6$ |
| 61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 1]$ | $\phantom{-}2e - 6$ |
| 79 | $[79, 79, \frac{3}{4}w^{3} - \frac{25}{4}w - \frac{9}{2}]$ | $-2e + 4$ |
| 79 | $[79, 79, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{3}{4}w - \frac{3}{2}]$ | $-2e + 4$ |
| 79 | $[79, 79, \frac{1}{4}w^{3} - \frac{3}{4}w - \frac{9}{2}]$ | $-2e + 4$ |
| 79 | $[79, 79, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 13w - 3]$ | $-2e + 4$ |
| 101 | $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{7}{4}w - \frac{5}{2}]$ | $\phantom{-}2e - 14$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4,2,w]$ | $-1$ |
| $4$ | $[4,2,-\frac{1}{2}w^{3}+\frac{9}{2}w]$ | $-1$ |