Base field 4.4.13968.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 4\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13,13,-\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ |
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:
\(x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 1]$ | $\phantom{-}e$ |
2 | $[2, 2, -\frac{1}{2}w^{2} + \frac{3}{2}w]$ | $\phantom{-}1$ |
9 | $[9, 3, -\frac{1}{2}w^{2} + \frac{1}{2}w + 2]$ | $-2$ |
13 | $[13, 13, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 2]$ | $-e - 3$ |
13 | $[13, 13, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $\phantom{-}1$ |
23 | $[23, 23, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w]$ | $-e + 7$ |
23 | $[23, 23, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 3]$ | $-2e - 2$ |
37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 3w - 3]$ | $-e + 5$ |
37 | $[37, 37, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 6]$ | $\phantom{-}2e$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{7}{2}w]$ | $\phantom{-}4e + 4$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 3]$ | $\phantom{-}2e - 10$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 7w - 7]$ | $-2e$ |
61 | $[61, 61, w^{3} - w^{2} - 6w + 3]$ | $\phantom{-}4e + 2$ |
61 | $[61, 61, w^{3} - 2w^{2} - 5w + 3]$ | $-2e - 8$ |
61 | $[61, 61, w^{3} - w^{2} - 8w + 1]$ | $-2e - 4$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 5]$ | $-3e - 3$ |
71 | $[71, 71, -w^{3} + \frac{3}{2}w^{2} + \frac{15}{2}w - 6]$ | $-e - 9$ |
83 | $[83, 83, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 2w - 7]$ | $\phantom{-}e + 1$ |
83 | $[83, 83, \frac{1}{2}w^{3} - \frac{7}{2}w - 4]$ | $-4e + 4$ |
97 | $[97, 97, 2w - 1]$ | $-6e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13,13,-\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w - 1]$ | $-1$ |