Base field \(\Q(\sqrt{165}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 41\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 3, 3]$ |
| 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:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, 2]$ | $-3$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 5]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w + 1]$ | $-e$ |
| 13 | $[13, 13, w + 11]$ | $-e$ |
| 23 | $[23, 23, w + 10]$ | $\phantom{-}6$ |
| 23 | $[23, 23, w + 12]$ | $-6$ |
| 29 | $[29, 29, -w - 3]$ | $-3e$ |
| 29 | $[29, 29, w - 4]$ | $\phantom{-}3e$ |
| 31 | $[31, 31, -w - 8]$ | $\phantom{-}0$ |
| 31 | $[31, 31, w - 9]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -w]$ | $\phantom{-}3e$ |
| 41 | $[41, 41, w - 1]$ | $-3e$ |
| 43 | $[43, 43, w + 18]$ | $-e$ |
| 43 | $[43, 43, w + 24]$ | $-e$ |
| 47 | $[47, 47, w + 13]$ | $\phantom{-}6$ |
| 47 | $[47, 47, w + 33]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 1]$ | $-1$ |