Base field \(\Q(\zeta_{20})^+\)
Generator \(w\), with minimal polynomial \(x^{4} - 5x^{2} + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[59,59,2w^{2} - w - 7]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{3} - w^{2} + 3w + 4]$ | $\phantom{-}3$ |
| 5 | $[5, 5, w]$ | $-1$ |
| 19 | $[19, 19, -w^{2} + w + 4]$ | $\phantom{-}6$ |
| 19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $-3$ |
| 19 | $[19, 19, -w^{3} - w^{2} + 3w + 1]$ | $\phantom{-}3$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}0$ |
| 41 | $[41, 41, w + 3]$ | $-5$ |
| 41 | $[41, 41, -w^{3} + 3w + 3]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{3} + 3w - 3]$ | $\phantom{-}4$ |
| 41 | $[41, 41, w - 3]$ | $-2$ |
| 59 | $[59, 59, 2w^{2} + w - 7]$ | $\phantom{-}9$ |
| 59 | $[59, 59, -w^{3} - 2w^{2} + 3w + 3]$ | $-3$ |
| 59 | $[59, 59, 2w^{3} - w^{2} - 7w + 2]$ | $-6$ |
| 59 | $[59, 59, w^{3} - w^{2} - w + 3]$ | $-1$ |
| 61 | $[61, 61, 3w^{2} - w - 8]$ | $-12$ |
| 61 | $[61, 61, w^{3} + 3w^{2} - 3w - 7]$ | $-9$ |
| 61 | $[61, 61, -w^{3} + 3w^{2} + 3w - 7]$ | $\phantom{-}6$ |
| 61 | $[61, 61, -3w^{2} - w + 8]$ | $-3$ |
| 79 | $[79, 79, -w^{3} + 2w^{2} + 2w - 6]$ | $\phantom{-}9$ |
| 79 | $[79, 79, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59,59,2w^{2} - w - 7]$ | $1$ |