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: | $[400, 20, 20]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, 2]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -2 w + 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -3 w + 2]$ | $\phantom{-}0$ |
| 11 | $[11, 11, -3 w + 1]$ | $\phantom{-}0$ |
| 19 | $[19, 19, -4 w + 3]$ | $\phantom{-}4$ |
| 19 | $[19, 19, -4 w + 1]$ | $\phantom{-}4$ |
| 29 | $[29, 29, w + 5]$ | $-6$ |
| 29 | $[29, 29, -w + 6]$ | $-6$ |
| 31 | $[31, 31, -5 w + 2]$ | $-4$ |
| 31 | $[31, 31, -5 w + 3]$ | $-4$ |
| 41 | $[41, 41, -6 w + 5]$ | $\phantom{-}6$ |
| 41 | $[41, 41, w - 7]$ | $\phantom{-}6$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}10$ |
| 59 | $[59, 59, 2 w - 9]$ | $-12$ |
| 59 | $[59, 59, 7 w - 5]$ | $-12$ |
| 61 | $[61, 61, 3 w - 10]$ | $\phantom{-}2$ |
| 61 | $[61, 61, -3 w - 7]$ | $\phantom{-}2$ |
| 71 | $[71, 71, -8 w + 7]$ | $-12$ |
| 71 | $[71, 71, w - 9]$ | $-12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, 2]$ | $1$ |
| $5$ | $[5, 5, -2 w + 1]$ | $1$ |