Base field \(\Q(\sqrt{11}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 11\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[338, 26, 13w - 39]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $96$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 3]$ | $\phantom{-}1$ |
| 5 | $[5, 5, w - 4]$ | $-1$ |
| 5 | $[5, 5, -w - 4]$ | $-1$ |
| 7 | $[7, 7, w + 2]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w - 2]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}3$ |
| 11 | $[11, 11, -w]$ | $-2$ |
| 19 | $[19, 19, 2w - 5]$ | $\phantom{-}6$ |
| 19 | $[19, 19, -2w - 5]$ | $\phantom{-}6$ |
| 37 | $[37, 37, 2w - 9]$ | $\phantom{-}3$ |
| 37 | $[37, 37, -2w - 9]$ | $\phantom{-}3$ |
| 43 | $[43, 43, 2w - 1]$ | $-5$ |
| 43 | $[43, 43, -2w - 1]$ | $-5$ |
| 53 | $[53, 53, -w - 8]$ | $\phantom{-}12$ |
| 53 | $[53, 53, w - 8]$ | $\phantom{-}12$ |
| 79 | $[79, 79, 5w - 14]$ | $-4$ |
| 79 | $[79, 79, 8w - 25]$ | $-4$ |
| 83 | $[83, 83, -3w - 4]$ | $\phantom{-}0$ |
| 83 | $[83, 83, 3w - 4]$ | $\phantom{-}0$ |
| 89 | $[89, 89, -w - 10]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 3]$ | $-1$ |
| $169$ | $[169, 13, -13]$ | $-1$ |