Base field \(\Q(\sqrt{33}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[324, 18, 18]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $-1$ |
| 2 | $[2, 2, -w + 3]$ | $-1$ |
| 3 | $[3, 3, 2w - 7]$ | $\phantom{-}0$ |
| 11 | $[11, 11, 4w - 13]$ | $-3$ |
| 17 | $[17, 17, -2w + 5]$ | $\phantom{-}0$ |
| 17 | $[17, 17, 2w + 3]$ | $\phantom{-}0$ |
| 25 | $[25, 5, 5]$ | $-1$ |
| 29 | $[29, 29, -2w + 3]$ | $\phantom{-}6$ |
| 29 | $[29, 29, 2w + 1]$ | $\phantom{-}6$ |
| 31 | $[31, 31, -2w + 9]$ | $\phantom{-}5$ |
| 31 | $[31, 31, 2w + 7]$ | $\phantom{-}5$ |
| 37 | $[37, 37, -4w - 11]$ | $\phantom{-}2$ |
| 37 | $[37, 37, 4w - 15]$ | $\phantom{-}2$ |
| 41 | $[41, 41, -10w + 33]$ | $-6$ |
| 41 | $[41, 41, 6w - 19]$ | $-6$ |
| 49 | $[49, 7, -7]$ | $-13$ |
| 67 | $[67, 67, 2w - 11]$ | $\phantom{-}14$ |
| 67 | $[67, 67, -2w - 9]$ | $\phantom{-}14$ |
| 83 | $[83, 83, 4w + 5]$ | $-3$ |
| 83 | $[83, 83, 4w - 9]$ | $-3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $1$ |
| $2$ | $[2, 2, -w + 3]$ | $1$ |
| $3$ | $[3, 3, 2w - 7]$ | $1$ |