Base field 4.4.16448.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 6x^{2} + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
5 | $[5, 5, -w^{3} + 3w^{2} + 2w - 1]$ | $-e + 2$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e + 3$ |
11 | $[11, 11, w^{3} - 2w^{2} - 5w - 1]$ | $-2e - 3$ |
13 | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ | $-1$ |
17 | $[17, 17, 2w^{3} - 5w^{2} - 9w + 5]$ | $\phantom{-}4e + 6$ |
23 | $[23, 23, -w^{3} + 3w^{2} + 4w - 5]$ | $-e - 1$ |
25 | $[25, 5, -w^{2} + 3w + 1]$ | $\phantom{-}5$ |
29 | $[29, 29, -2w^{3} + 6w^{2} + 5w - 1]$ | $-e - 2$ |
31 | $[31, 31, -w^{2} + 2w + 1]$ | $-e + 7$ |
43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 3]$ | $-5$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 6w - 3]$ | $\phantom{-}2e + 3$ |
59 | $[59, 59, 2w^{3} - 6w^{2} - 7w + 7]$ | $-5e - 9$ |
73 | $[73, 73, 3w^{3} - 6w^{2} - 16w - 5]$ | $-6e - 6$ |
79 | $[79, 79, -5w^{3} + 14w^{2} + 20w - 17]$ | $\phantom{-}6e + 6$ |
81 | $[81, 3, -3]$ | $\phantom{-}5e + 11$ |
83 | $[83, 83, -w - 3]$ | $\phantom{-}2e + 8$ |
83 | $[83, 83, w^{2} - 3w - 7]$ | $\phantom{-}2e + 1$ |
89 | $[89, 89, w^{2} - 2w - 7]$ | $-5e - 7$ |
101 | $[101, 101, -2w^{3} + 5w^{2} + 8w - 3]$ | $\phantom{-}4e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, -w^{3} + 3w^{2} + 3w - 1]$ | $1$ |