Base field \(\Q(\sqrt{23}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 23\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[18, 6, -3w - 15]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
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 |
|---|---|---|
| 2 | $[2, 2, -w - 5]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -w + 4]$ | $-e$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}e$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -2w + 9]$ | $-2e$ |
| 11 | $[11, 11, -2w - 9]$ | $\phantom{-}2e$ |
| 13 | $[13, 13, w + 6]$ | $\phantom{-}6$ |
| 13 | $[13, 13, -w + 6]$ | $\phantom{-}6$ |
| 19 | $[19, 19, -w - 2]$ | $\phantom{-}3e$ |
| 19 | $[19, 19, w - 2]$ | $-3e$ |
| 23 | $[23, 23, -w]$ | $\phantom{-}0$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}2$ |
| 29 | $[29, 29, 7w + 34]$ | $-2$ |
| 29 | $[29, 29, 2w + 11]$ | $-2$ |
| 41 | $[41, 41, -w - 8]$ | $-6$ |
| 41 | $[41, 41, w - 8]$ | $-6$ |
| 43 | $[43, 43, 2w - 7]$ | $-e$ |
| 43 | $[43, 43, -2w - 7]$ | $\phantom{-}e$ |
| 67 | $[67, 67, 2w - 5]$ | $-3e$ |
| 67 | $[67, 67, -2w - 5]$ | $\phantom{-}3e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 5]$ | $-1$ |
| $9$ | $[9, 3, 3]$ | $-1$ |