Base field \(\Q(\sqrt{10}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 10\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[135, 45, -3w - 15]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
3 | $[3, 3, w + 1]$ | $-1$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}0$ |
5 | $[5, 5, w]$ | $\phantom{-}1$ |
13 | $[13, 13, w + 6]$ | $-2$ |
13 | $[13, 13, w + 7]$ | $\phantom{-}4$ |
31 | $[31, 31, -2w + 3]$ | $-4$ |
31 | $[31, 31, 2w + 3]$ | $-4$ |
37 | $[37, 37, w + 11]$ | $-2$ |
37 | $[37, 37, w + 26]$ | $-8$ |
41 | $[41, 41, 3w + 7]$ | $-6$ |
41 | $[41, 41, -3w + 7]$ | $-12$ |
43 | $[43, 43, w + 15]$ | $\phantom{-}4$ |
43 | $[43, 43, w + 28]$ | $-8$ |
49 | $[49, 7, -7]$ | $\phantom{-}2$ |
53 | $[53, 53, w + 13]$ | $\phantom{-}6$ |
53 | $[53, 53, w + 40]$ | $\phantom{-}6$ |
67 | $[67, 67, w + 12]$ | $\phantom{-}4$ |
67 | $[67, 67, w + 55]$ | $\phantom{-}4$ |
71 | $[71, 71, -w - 9]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$3$ | $[3, 3, w + 2]$ | $1$ |
$5$ | $[5, 5, w]$ | $-1$ |