Base field \(\Q(\sqrt{119}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 119\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[2, 2, -w + 11]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 11]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $-4$ |
| 11 | $[11, 11, w + 3]$ | $\phantom{-}3e$ |
| 11 | $[11, 11, w + 8]$ | $-3e$ |
| 17 | $[17, 17, w]$ | $-4e$ |
| 19 | $[19, 19, w - 10]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -w - 10]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w + 2]$ | $-6e$ |
| 23 | $[23, 23, w + 21]$ | $\phantom{-}6e$ |
| 41 | $[41, 41, w + 18]$ | $-8e$ |
| 41 | $[41, 41, w + 23]$ | $-8e$ |
| 47 | $[47, 47, -3w + 32]$ | $-6$ |
| 47 | $[47, 47, 8w - 87]$ | $\phantom{-}6$ |
| 53 | $[53, 53, -2w + 23]$ | $-6$ |
| 53 | $[53, 53, -13w + 142]$ | $-6$ |
| 59 | $[59, 59, -5w + 54]$ | $\phantom{-}12$ |
| 59 | $[59, 59, 6w - 65]$ | $-12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 11]$ | $-1$ |