Base field \(\Q(\sqrt{209}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 52\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[10,10,-7w + 54]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -11w - 74]$ | $-1$ |
2 | $[2, 2, -11w + 85]$ | $-2$ |
5 | $[5, 5, 4w - 31]$ | $-1$ |
5 | $[5, 5, -4w - 27]$ | $\phantom{-}1$ |
9 | $[9, 3, 3]$ | $\phantom{-}1$ |
11 | $[11, 11, -70w - 471]$ | $\phantom{-}1$ |
13 | $[13, 13, -2w - 13]$ | $\phantom{-}0$ |
13 | $[13, 13, -2w + 15]$ | $-4$ |
19 | $[19, 19, 92w - 711]$ | $\phantom{-}0$ |
23 | $[23, 23, -26w + 201]$ | $\phantom{-}1$ |
23 | $[23, 23, -26w - 175]$ | $-3$ |
29 | $[29, 29, 18w - 139]$ | $-6$ |
29 | $[29, 29, 18w + 121]$ | $\phantom{-}8$ |
41 | $[41, 41, -10w - 67]$ | $-6$ |
41 | $[41, 41, 10w - 77]$ | $-12$ |
47 | $[47, 47, 2w - 17]$ | $\phantom{-}7$ |
47 | $[47, 47, 2w + 15]$ | $\phantom{-}9$ |
49 | $[49, 7, -7]$ | $\phantom{-}9$ |
79 | $[79, 79, 40w - 309]$ | $\phantom{-}4$ |
79 | $[79, 79, 40w + 269]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,11w + 74]$ | $1$ |
$5$ | $[5,5,-4w - 27]$ | $-1$ |