Base field \(\Q(\sqrt{137}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 34\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 3w + 16]$ | $\phantom{-}e$ |
| 2 | $[2, 2, 3w - 19]$ | $-e$ |
| 7 | $[7, 7, -2w - 11]$ | $-2e - 1$ |
| 7 | $[7, 7, 2w - 13]$ | $\phantom{-}2e - 1$ |
| 9 | $[9, 3, 3]$ | $-1$ |
| 11 | $[11, 11, 14w + 75]$ | $-2$ |
| 11 | $[11, 11, -14w + 89]$ | $-2$ |
| 17 | $[17, 17, 8w - 51]$ | $-2e - 4$ |
| 17 | $[17, 17, 8w + 43]$ | $\phantom{-}2e - 4$ |
| 19 | $[19, 19, -4w + 25]$ | $\phantom{-}2e + 1$ |
| 19 | $[19, 19, -4w - 21]$ | $-2e + 1$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}1$ |
| 37 | $[37, 37, -2w + 11]$ | $\phantom{-}5$ |
| 37 | $[37, 37, 2w + 9]$ | $\phantom{-}5$ |
| 59 | $[59, 59, 2w - 15]$ | $-2e - 2$ |
| 59 | $[59, 59, 2w + 13]$ | $\phantom{-}2e - 2$ |
| 61 | $[61, 61, -10w + 63]$ | $\phantom{-}9$ |
| 61 | $[61, 61, -10w - 53]$ | $\phantom{-}9$ |
| 73 | $[73, 73, 2w - 9]$ | $-4e + 9$ |
| 73 | $[73, 73, -2w - 7]$ | $\phantom{-}4e + 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, 3]$ | $1$ |