Base field \(\Q(\sqrt{6}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[392, 28, 14w - 28]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $\phantom{-}0$ |
3 | $[3, 3, w - 3]$ | $\phantom{-}0$ |
5 | $[5, 5, w + 1]$ | $-2$ |
5 | $[5, 5, w - 1]$ | $-2$ |
19 | $[19, 19, w + 5]$ | $\phantom{-}8$ |
19 | $[19, 19, -w + 5]$ | $\phantom{-}8$ |
23 | $[23, 23, -2w + 1]$ | $\phantom{-}0$ |
23 | $[23, 23, -2w - 1]$ | $\phantom{-}0$ |
29 | $[29, 29, -3w + 5]$ | $-6$ |
29 | $[29, 29, -3w - 5]$ | $-6$ |
43 | $[43, 43, -w - 7]$ | $-4$ |
43 | $[43, 43, w - 7]$ | $-4$ |
47 | $[47, 47, 4w - 7]$ | $\phantom{-}8$ |
47 | $[47, 47, 6w - 13]$ | $\phantom{-}8$ |
49 | $[49, 7, -7]$ | $\phantom{-}1$ |
53 | $[53, 53, -3w - 1]$ | $-6$ |
53 | $[53, 53, 3w - 1]$ | $-6$ |
67 | $[67, 67, -7w + 19]$ | $-4$ |
67 | $[67, 67, -3w + 11]$ | $-4$ |
71 | $[71, 71, -4w - 5]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 2]$ | $1$ |
$49$ | $[49, 7, -7]$ | $-1$ |