Base field \(\Q(\sqrt{217}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 54\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[28, 14, 996w - 7834]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $58$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 8]$ | $-1$ |
2 | $[2, 2, w + 7]$ | $-1$ |
3 | $[3, 3, -52w - 357]$ | $\phantom{-}2$ |
3 | $[3, 3, -52w + 409]$ | $\phantom{-}2$ |
7 | $[7, 7, 498w - 3917]$ | $\phantom{-}1$ |
13 | $[13, 13, 22w - 173]$ | $\phantom{-}4$ |
13 | $[13, 13, 22w + 151]$ | $\phantom{-}4$ |
17 | $[17, 17, -6w - 41]$ | $-6$ |
17 | $[17, 17, -6w + 47]$ | $-6$ |
25 | $[25, 5, -5]$ | $-10$ |
31 | $[31, 31, 1048w - 8243]$ | $\phantom{-}4$ |
61 | $[61, 61, 602w - 4735]$ | $-8$ |
61 | $[61, 61, 602w + 4133]$ | $-8$ |
67 | $[67, 67, -186w - 1277]$ | $-4$ |
67 | $[67, 67, -186w + 1463]$ | $-4$ |
71 | $[71, 71, 290w - 2281]$ | $\phantom{-}0$ |
71 | $[71, 71, 290w + 1991]$ | $\phantom{-}0$ |
73 | $[73, 73, 2w - 13]$ | $-2$ |
73 | $[73, 73, -2w - 11]$ | $-2$ |
83 | $[83, 83, -36w - 247]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 8]$ | $1$ |
$2$ | $[2, 2, w + 7]$ | $1$ |
$7$ | $[7, 7, 498w - 3917]$ | $-1$ |