Base field \(\Q(\sqrt{13}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[675,45,15w - 15]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w]$ | $\phantom{-}1$ |
3 | $[3, 3, -w + 1]$ | $\phantom{-}0$ |
4 | $[4, 2, 2]$ | $\phantom{-}1$ |
13 | $[13, 13, -2w + 1]$ | $\phantom{-}2$ |
17 | $[17, 17, w + 4]$ | $\phantom{-}4$ |
17 | $[17, 17, -w + 5]$ | $\phantom{-}6$ |
23 | $[23, 23, 3w + 1]$ | $-4$ |
23 | $[23, 23, -3w + 4]$ | $-4$ |
25 | $[25, 5, 5]$ | $\phantom{-}1$ |
29 | $[29, 29, 3w - 2]$ | $-2$ |
29 | $[29, 29, -3w + 1]$ | $\phantom{-}0$ |
43 | $[43, 43, -4w - 1]$ | $\phantom{-}4$ |
43 | $[43, 43, 4w - 5]$ | $\phantom{-}12$ |
49 | $[49, 7, -7]$ | $\phantom{-}6$ |
53 | $[53, 53, -w - 7]$ | $\phantom{-}2$ |
53 | $[53, 53, w - 8]$ | $-4$ |
61 | $[61, 61, -3w - 8]$ | $-14$ |
61 | $[61, 61, 3w - 11]$ | $\phantom{-}10$ |
79 | $[79, 79, 5w - 4]$ | $\phantom{-}4$ |
79 | $[79, 79, 5w - 1]$ | $\phantom{-}8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,w - 1]$ | $1$ |
$3$ | $[3,3,w]$ | $-1$ |
$25$ | $[25,5,5]$ | $-1$ |