Base field \(\Q(\sqrt{89}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 22\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[89, 89, 2w - 1]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $191$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 4]$ | $-1$ |
| 2 | $[2, 2, -w + 5]$ | $-1$ |
| 5 | $[5, 5, 4w - 21]$ | $-1$ |
| 5 | $[5, 5, -4w - 17]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $-5$ |
| 11 | $[11, 11, 2w - 11]$ | $-2$ |
| 11 | $[11, 11, -2w - 9]$ | $-2$ |
| 17 | $[17, 17, -6w - 25]$ | $\phantom{-}3$ |
| 17 | $[17, 17, -6w + 31]$ | $\phantom{-}3$ |
| 47 | $[47, 47, 24w + 101]$ | $-12$ |
| 47 | $[47, 47, 24w - 125]$ | $-12$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2$ |
| 53 | $[53, 53, 2w - 7]$ | $-3$ |
| 53 | $[53, 53, -2w - 5]$ | $-3$ |
| 67 | $[67, 67, 4w - 19]$ | $\phantom{-}12$ |
| 67 | $[67, 67, 4w + 15]$ | $\phantom{-}12$ |
| 71 | $[71, 71, 16w - 83]$ | $-10$ |
| 71 | $[71, 71, 16w + 67]$ | $-10$ |
| 73 | $[73, 73, 2w - 5]$ | $\phantom{-}7$ |
| 73 | $[73, 73, -2w - 3]$ | $\phantom{-}7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $89$ | $[89, 89, 2w - 1]$ | $1$ |