Base field \(\Q(\sqrt{22}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 22\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[32, 8, -12w + 56]$ |
| Dimension: | $1$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w + 14]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w + 5]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 2w + 9]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 2w - 9]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -7w + 33]$ | $\phantom{-}0$ |
| 13 | $[13, 13, -w - 3]$ | $-6$ |
| 13 | $[13, 13, -w + 3]$ | $-6$ |
| 25 | $[25, 5, -5]$ | $-6$ |
| 29 | $[29, 29, 3w + 13]$ | $\phantom{-}10$ |
| 29 | $[29, 29, -3w + 13]$ | $\phantom{-}10$ |
| 59 | $[59, 59, -w - 9]$ | $\phantom{-}0$ |
| 59 | $[59, 59, w - 9]$ | $\phantom{-}0$ |
| 61 | $[61, 61, 11w - 51]$ | $\phantom{-}10$ |
| 61 | $[61, 61, 25w - 117]$ | $\phantom{-}10$ |
| 67 | $[67, 67, 9w - 43]$ | $\phantom{-}0$ |
| 67 | $[67, 67, -9w - 43]$ | $\phantom{-}0$ |
| 79 | $[79, 79, 2w - 3]$ | $\phantom{-}0$ |
| 79 | $[79, 79, -2w - 3]$ | $\phantom{-}0$ |
| 89 | $[89, 89, 4w - 21]$ | $\phantom{-}10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -3w + 14]$ | $1$ |