Base field \(\Q(\sqrt{7}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[338, 26, -13w + 39]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 3]$ | $\phantom{-}1$ |
3 | $[3, 3, w - 2]$ | $-3$ |
3 | $[3, 3, w + 2]$ | $-3$ |
7 | $[7, 7, w]$ | $\phantom{-}1$ |
19 | $[19, 19, 2w - 3]$ | $\phantom{-}6$ |
19 | $[19, 19, 2w + 3]$ | $\phantom{-}6$ |
25 | $[25, 5, 5]$ | $-9$ |
29 | $[29, 29, -w - 6]$ | $\phantom{-}2$ |
29 | $[29, 29, w - 6]$ | $\phantom{-}2$ |
31 | $[31, 31, 4w + 9]$ | $\phantom{-}4$ |
31 | $[31, 31, -4w + 9]$ | $\phantom{-}4$ |
37 | $[37, 37, -3w + 10]$ | $\phantom{-}3$ |
37 | $[37, 37, -6w + 17]$ | $\phantom{-}3$ |
47 | $[47, 47, -3w - 4]$ | $\phantom{-}13$ |
47 | $[47, 47, 3w - 4]$ | $\phantom{-}13$ |
53 | $[53, 53, 2w - 9]$ | $\phantom{-}12$ |
53 | $[53, 53, 2w + 9]$ | $\phantom{-}12$ |
59 | $[59, 59, 3w - 2]$ | $-10$ |
59 | $[59, 59, -3w - 2]$ | $-10$ |
83 | $[83, 83, -6w - 13]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w - 3]$ | $-1$ |
$169$ | $[169, 13, -13]$ | $-1$ |