Base field \(\Q(\sqrt{61}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 15\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[225, 15, 15]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $63$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w - 3]$ | $-1$ |
3 | $[3, 3, -w + 4]$ | $-1$ |
4 | $[4, 2, 2]$ | $-3$ |
5 | $[5, 5, w - 5]$ | $\phantom{-}1$ |
5 | $[5, 5, -w - 4]$ | $\phantom{-}1$ |
13 | $[13, 13, -w - 1]$ | $-2$ |
13 | $[13, 13, w - 2]$ | $-2$ |
19 | $[19, 19, 3w - 14]$ | $\phantom{-}4$ |
19 | $[19, 19, -3w - 11]$ | $\phantom{-}4$ |
41 | $[41, 41, -w - 7]$ | $\phantom{-}10$ |
41 | $[41, 41, w - 8]$ | $\phantom{-}10$ |
47 | $[47, 47, 3w - 11]$ | $\phantom{-}8$ |
47 | $[47, 47, -3w - 8]$ | $\phantom{-}8$ |
49 | $[49, 7, -7]$ | $-14$ |
61 | $[61, 61, 2w - 1]$ | $-2$ |
73 | $[73, 73, -3w + 16]$ | $\phantom{-}10$ |
73 | $[73, 73, 3w + 13]$ | $\phantom{-}10$ |
83 | $[83, 83, 2w - 13]$ | $\phantom{-}12$ |
83 | $[83, 83, -2w - 11]$ | $\phantom{-}12$ |
97 | $[97, 97, 7w + 22]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w - 3]$ | $1$ |
$3$ | $[3, 3, -w + 4]$ | $1$ |
$5$ | $[5, 5, w - 5]$ | $-1$ |
$5$ | $[5, 5, -w - 4]$ | $-1$ |