Base field \(\Q(\sqrt{161}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 40\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[28, 14, 64w - 438]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 6]$ | $-1$ |
2 | $[2, 2, -w + 7]$ | $-1$ |
5 | $[5, 5, -6w - 35]$ | $\phantom{-}0$ |
5 | $[5, 5, -6w + 41]$ | $\phantom{-}0$ |
7 | $[7, 7, 32w - 219]$ | $-1$ |
9 | $[9, 3, 3]$ | $-2$ |
17 | $[17, 17, 2w - 13]$ | $-6$ |
17 | $[17, 17, 2w + 11]$ | $-6$ |
19 | $[19, 19, 4w + 23]$ | $-2$ |
19 | $[19, 19, 4w - 27]$ | $-2$ |
23 | $[23, 23, 58w - 397]$ | $\phantom{-}0$ |
29 | $[29, 29, 20w - 137]$ | $-6$ |
29 | $[29, 29, -20w - 117]$ | $-6$ |
61 | $[61, 61, 2w - 11]$ | $-8$ |
61 | $[61, 61, -2w - 9]$ | $-8$ |
71 | $[71, 71, -10w - 59]$ | $\phantom{-}0$ |
71 | $[71, 71, 10w - 69]$ | $\phantom{-}0$ |
83 | $[83, 83, -44w + 301]$ | $\phantom{-}6$ |
83 | $[83, 83, 44w + 257]$ | $\phantom{-}6$ |
89 | $[89, 89, -70w - 409]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 6]$ | $1$ |
$2$ | $[2, 2, -w + 7]$ | $1$ |
$7$ | $[7, 7, 32w - 219]$ | $1$ |