Base field \(\Q(\sqrt{457}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 114\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[6, 6, -53w - 540]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $65$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -6987w + 78176]$ | $-1$ |
| 2 | $[2, 2, -6987w - 71189]$ | $-1$ |
| 3 | $[3, 3, -196w + 2193]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -196w - 1997]$ | $\phantom{-}2$ |
| 7 | $[7, 7, -16w - 163]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -16w + 179]$ | $-4$ |
| 17 | $[17, 17, 6w - 67]$ | $\phantom{-}0$ |
| 17 | $[17, 17, 6w + 61]$ | $\phantom{-}6$ |
| 19 | $[19, 19, -90w + 1007]$ | $-2$ |
| 19 | $[19, 19, 90w + 917]$ | $\phantom{-}0$ |
| 25 | $[25, 5, -5]$ | $-2$ |
| 29 | $[29, 29, -11140w + 124643]$ | $-4$ |
| 29 | $[29, 29, -11140w - 113503]$ | $\phantom{-}6$ |
| 47 | $[47, 47, 53062w + 540637]$ | $\phantom{-}8$ |
| 47 | $[47, 47, 53062w - 593699]$ | $-2$ |
| 67 | $[67, 67, 2442w - 27323]$ | $\phantom{-}2$ |
| 67 | $[67, 67, 2442w + 24881]$ | $\phantom{-}12$ |
| 73 | $[73, 73, 302w + 3077]$ | $-16$ |
| 73 | $[73, 73, 302w - 3379]$ | $\phantom{-}4$ |
| 79 | $[79, 79, 94984w + 967771]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -6987w + 78176]$ | $1$ |
| $3$ | $[3, 3, -196w + 2193]$ | $-1$ |