Base field \(\Q(\sqrt{38}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 38\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[38, 38, w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $64$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 6]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $-5$ |
| 11 | $[11, 11, -w + 7]$ | $-6$ |
| 11 | $[11, 11, w + 7]$ | $-6$ |
| 13 | $[13, 13, -w - 5]$ | $-5$ |
| 13 | $[13, 13, w - 5]$ | $-5$ |
| 17 | $[17, 17, -2w + 13]$ | $\phantom{-}3$ |
| 17 | $[17, 17, -2w - 13]$ | $\phantom{-}3$ |
| 19 | $[19, 19, -3w + 19]$ | $\phantom{-}1$ |
| 25 | $[25, 5, 5]$ | $-10$ |
| 29 | $[29, 29, -w - 3]$ | $-9$ |
| 29 | $[29, 29, w - 3]$ | $-9$ |
| 31 | $[31, 31, -2w + 11]$ | $\phantom{-}4$ |
| 31 | $[31, 31, -8w + 49]$ | $\phantom{-}4$ |
| 37 | $[37, 37, -w - 1]$ | $-2$ |
| 37 | $[37, 37, w - 1]$ | $-2$ |
| 43 | $[43, 43, -w - 9]$ | $\phantom{-}8$ |
| 43 | $[43, 43, w - 9]$ | $\phantom{-}8$ |
| 49 | $[49, 7, -7]$ | $-13$ |
| 53 | $[53, 53, -3w + 17]$ | $\phantom{-}3$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 6]$ | $-1$ |
| $19$ | $[19, 19, -3w + 19]$ | $-1$ |