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: | $[19, 19, w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -3 w - 13]$ | $\phantom{-}0$ |
| 3 | $[3, 3, w + 4]$ | $\phantom{-}2$ |
| 3 | $[3, 3, w - 4]$ | $\phantom{-}2$ |
| 5 | $[5, 5, 2 w + 9]$ | $\phantom{-}3$ |
| 5 | $[5, 5, -2 w + 9]$ | $\phantom{-}3$ |
| 17 | $[17, 17, w + 6]$ | $-3$ |
| 17 | $[17, 17, -w + 6]$ | $-3$ |
| 19 | $[19, 19, w]$ | $-1$ |
| 31 | $[31, 31, 20 w + 87]$ | $\phantom{-}4$ |
| 31 | $[31, 31, 7 w + 30]$ | $\phantom{-}4$ |
| 49 | $[49, 7, -7]$ | $-13$ |
| 59 | $[59, 59, 6 w + 25]$ | $\phantom{-}6$ |
| 59 | $[59, 59, -6 w + 25]$ | $\phantom{-}6$ |
| 61 | $[61, 61, -9 w - 40]$ | $-1$ |
| 61 | $[61, 61, 9 w - 40]$ | $-1$ |
| 67 | $[67, 67, 2 w - 3]$ | $\phantom{-}4$ |
| 67 | $[67, 67, -2 w - 3]$ | $\phantom{-}4$ |
| 71 | $[71, 71, 3 w + 10]$ | $-6$ |
| 71 | $[71, 71, 3 w - 10]$ | $-6$ |
| 73 | $[73, 73, 27 w + 118]$ | $-7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, w]$ | $1$ |