Base field \(\Q(\sqrt{17}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[361, 19, 19]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $55$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $-2$ |
| 13 | $[13, 13, -2w + 3]$ | $-4$ |
| 13 | $[13, 13, 2w + 1]$ | $-4$ |
| 17 | $[17, 17, -2w + 1]$ | $-3$ |
| 19 | $[19, 19, -2w + 7]$ | $\phantom{-}1$ |
| 19 | $[19, 19, 2w + 5]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -5]$ | $-1$ |
| 43 | $[43, 43, 4w - 7]$ | $-1$ |
| 43 | $[43, 43, 4w + 3]$ | $-1$ |
| 47 | $[47, 47, -2w + 9]$ | $-3$ |
| 47 | $[47, 47, 2w + 7]$ | $-3$ |
| 49 | $[49, 7, -7]$ | $-13$ |
| 53 | $[53, 53, 4w - 13]$ | $\phantom{-}12$ |
| 53 | $[53, 53, 6w - 13]$ | $\phantom{-}12$ |
| 59 | $[59, 59, -4w - 1]$ | $-6$ |
| 59 | $[59, 59, 4w - 5]$ | $-6$ |
| 67 | $[67, 67, 4w - 3]$ | $-4$ |
| 67 | $[67, 67, 4w - 1]$ | $-4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -2w + 7]$ | $-1$ |
| $19$ | $[19, 19, 2w + 5]$ | $-1$ |