Base field \(\Q(\sqrt{53}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 13\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[625, 25, -25]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, 2]$ | $-1$ |
7 | $[7, 7, w + 2]$ | $-4$ |
7 | $[7, 7, w - 3]$ | $\phantom{-}4$ |
9 | $[9, 3, 3]$ | $\phantom{-}1$ |
11 | $[11, 11, w + 1]$ | $-2$ |
11 | $[11, 11, w - 2]$ | $\phantom{-}6$ |
13 | $[13, 13, w]$ | $\phantom{-}1$ |
13 | $[13, 13, w - 1]$ | $\phantom{-}5$ |
17 | $[17, 17, -w - 5]$ | $\phantom{-}7$ |
17 | $[17, 17, w - 6]$ | $\phantom{-}3$ |
25 | $[25, 5, -5]$ | $\phantom{-}0$ |
29 | $[29, 29, -w - 6]$ | $-5$ |
29 | $[29, 29, w - 7]$ | $\phantom{-}3$ |
37 | $[37, 37, 2w - 5]$ | $\phantom{-}3$ |
37 | $[37, 37, -2w - 3]$ | $-1$ |
43 | $[43, 43, -w - 7]$ | $\phantom{-}2$ |
43 | $[43, 43, w - 8]$ | $\phantom{-}2$ |
47 | $[47, 47, 3w + 7]$ | $\phantom{-}4$ |
47 | $[47, 47, 3w - 10]$ | $\phantom{-}4$ |
53 | $[53, 53, 2w - 1]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, -5]$ | $1$ |