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: | $[400,80,5 w - 25]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 2]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 13 | $[13, 13, -2 w + 3]$ | $\phantom{-}2$ |
| 13 | $[13, 13, 2 w + 1]$ | $-6$ |
| 17 | $[17, 17, -2 w + 1]$ | $-6$ |
| 19 | $[19, 19, -2 w + 7]$ | $-4$ |
| 19 | $[19, 19, 2 w + 5]$ | $\phantom{-}4$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}1$ |
| 43 | $[43, 43, 4 w - 7]$ | $\phantom{-}0$ |
| 43 | $[43, 43, 4 w + 3]$ | $-4$ |
| 47 | $[47, 47, -2 w + 9]$ | $\phantom{-}0$ |
| 47 | $[47, 47, 2 w + 7]$ | $-12$ |
| 49 | $[49, 7, -7]$ | $-6$ |
| 53 | $[53, 53, 4 w - 13]$ | $\phantom{-}6$ |
| 53 | $[53, 53, 6 w - 13]$ | $-10$ |
| 59 | $[59, 59, -4 w - 1]$ | $-4$ |
| 59 | $[59, 59, 4 w - 5]$ | $\phantom{-}4$ |
| 67 | $[67, 67, 4 w - 3]$ | $-8$ |
| 67 | $[67, 67, 4 w - 1]$ | $-4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,w + 1]$ | $1$ |
| $25$ | $[25,5,-5]$ | $-1$ |