Base field \(\Q(\sqrt{19}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[171, 57, 3w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $98$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3w - 13]$ | $-1$ |
| 3 | $[3, 3, w + 4]$ | $-1$ |
| 3 | $[3, 3, w - 4]$ | $-1$ |
| 5 | $[5, 5, 2w + 9]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -2w + 9]$ | $\phantom{-}4$ |
| 17 | $[17, 17, w + 6]$ | $-3$ |
| 17 | $[17, 17, -w + 6]$ | $\phantom{-}0$ |
| 19 | $[19, 19, w]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 20w + 87]$ | $\phantom{-}1$ |
| 31 | $[31, 31, 7w + 30]$ | $-8$ |
| 49 | $[49, 7, -7]$ | $-5$ |
| 59 | $[59, 59, 6w + 25]$ | $-3$ |
| 59 | $[59, 59, -6w + 25]$ | $-9$ |
| 61 | $[61, 61, -9w - 40]$ | $-5$ |
| 61 | $[61, 61, 9w - 40]$ | $\phantom{-}10$ |
| 67 | $[67, 67, 2w - 3]$ | $-2$ |
| 67 | $[67, 67, -2w - 3]$ | $\phantom{-}1$ |
| 71 | $[71, 71, 3w + 10]$ | $-12$ |
| 71 | $[71, 71, 3w - 10]$ | $\phantom{-}3$ |
| 73 | $[73, 73, 27w + 118]$ | $\phantom{-}13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w + 4]$ | $1$ |
| $3$ | $[3, 3, w - 4]$ | $1$ |
| $19$ | $[19, 19, w]$ | $-1$ |