Base field \(\Q(\sqrt{15}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 15\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 4, 2w + 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}2e$ |
| 7 | $[7, 7, w + 1]$ | $-e$ |
| 7 | $[7, 7, w + 6]$ | $-e$ |
| 11 | $[11, 11, -w - 2]$ | $\phantom{-}4$ |
| 11 | $[11, 11, w - 2]$ | $\phantom{-}4$ |
| 17 | $[17, 17, w + 7]$ | $\phantom{-}0$ |
| 17 | $[17, 17, w + 10]$ | $\phantom{-}0$ |
| 43 | $[43, 43, w + 12]$ | $-3e$ |
| 43 | $[43, 43, w + 31]$ | $-3e$ |
| 53 | $[53, 53, w + 11]$ | $\phantom{-}2e$ |
| 53 | $[53, 53, w + 42]$ | $\phantom{-}2e$ |
| 59 | $[59, 59, 2w - 1]$ | $-12$ |
| 59 | $[59, 59, -2w - 1]$ | $-12$ |
| 61 | $[61, 61, 2w - 11]$ | $-10$ |
| 61 | $[61, 61, -2w - 11]$ | $-10$ |
| 67 | $[67, 67, w + 22]$ | $-7e$ |
| 67 | $[67, 67, w + 45]$ | $-7e$ |
| 71 | $[71, 71, 3w - 8]$ | $-8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $\frac{1}{2}e$ |