Base field \(\Q(\sqrt{5}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight | [2, 2] |
| Level | $[3969, 63, -63]$ |
| Label | 2.2.5.1-3969.1-d |
| Dimension | 1 |
| Is CM | no |
| Is base change | yes |
| Parent newspace dimension | 56 |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $-3$ |
| 5 | $[5, 5, -2w + 1]$ | $\phantom{-}2$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -3w + 2]$ | $-4$ |
| 11 | $[11, 11, -3w + 1]$ | $-4$ |
| 19 | $[19, 19, -4w + 3]$ | $\phantom{-}4$ |
| 19 | $[19, 19, -4w + 1]$ | $\phantom{-}4$ |
| 29 | $[29, 29, w + 5]$ | $\phantom{-}2$ |
| 29 | $[29, 29, -w + 6]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -5w + 2]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -5w + 3]$ | $\phantom{-}0$ |
| 41 | $[41, 41, -6w + 5]$ | $-2$ |
| 41 | $[41, 41, w - 7]$ | $-2$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}1$ |
| 59 | $[59, 59, 2w - 9]$ | $-12$ |
| 59 | $[59, 59, 7w - 5]$ | $-12$ |
| 61 | $[61, 61, 3w - 10]$ | $-2$ |
| 61 | $[61, 61, -3w - 7]$ | $-2$ |
| 71 | $[71, 71, -8w + 7]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w - 9]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, 3]$ | $1$ |
| 49 | $[49, 7, -7]$ | $-1$ |