Base field \(\Q(\sqrt{77}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 19\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[77, 77, -2w + 1]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $62$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-4$ |
7 | $[7, 7, -w - 3]$ | $-1$ |
9 | $[9, 3, 3]$ | $-5$ |
11 | $[11, 11, w + 5]$ | $-1$ |
13 | $[13, 13, w + 2]$ | $\phantom{-}4$ |
13 | $[13, 13, w - 3]$ | $\phantom{-}4$ |
17 | $[17, 17, w + 1]$ | $\phantom{-}6$ |
17 | $[17, 17, -w + 2]$ | $\phantom{-}6$ |
19 | $[19, 19, w]$ | $-2$ |
19 | $[19, 19, w - 1]$ | $-2$ |
23 | $[23, 23, w + 6]$ | $\phantom{-}3$ |
23 | $[23, 23, -w + 7]$ | $\phantom{-}3$ |
25 | $[25, 5, -5]$ | $-1$ |
37 | $[37, 37, -w - 7]$ | $\phantom{-}11$ |
37 | $[37, 37, w - 8]$ | $\phantom{-}11$ |
41 | $[41, 41, 2w - 7]$ | $-6$ |
41 | $[41, 41, -2w - 5]$ | $-6$ |
53 | $[53, 53, -w - 8]$ | $-6$ |
53 | $[53, 53, w - 9]$ | $-6$ |
61 | $[61, 61, 2w - 5]$ | $\phantom{-}10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w - 3]$ | $1$ |
$11$ | $[11, 11, w + 5]$ | $1$ |