Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[13, 13, w^{2} - 3w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w^{2} - 2w - 4]$ | $\phantom{-}\frac{1}{2}e - 1$ |
7 | $[7, 7, w]$ | $\phantom{-}3$ |
7 | $[7, 7, w + 3]$ | $-e - 1$ |
7 | $[7, 7, -w^{2} + 2w + 3]$ | $\phantom{-}\frac{1}{2}e + 2$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e + 3$ |
13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}1$ |
17 | $[17, 17, w - 2]$ | $-e + 2$ |
25 | $[25, 5, -w^{2} - w + 3]$ | $\phantom{-}0$ |
29 | $[29, 29, w^{2} - 2w - 6]$ | $-e + 5$ |
31 | $[31, 31, w^{2} - 5]$ | $-\frac{3}{2}e$ |
37 | $[37, 37, -w^{2} - 2w + 2]$ | $\phantom{-}3$ |
41 | $[41, 41, w^{2} - 8]$ | $-e + 5$ |
43 | $[43, 43, w^{2} - w - 4]$ | $-\frac{3}{2}e - 3$ |
53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-\frac{3}{2}e - 3$ |
59 | $[59, 59, w^{2} - 3]$ | $\phantom{-}2e - 6$ |
59 | $[59, 59, w^{2} - 3w - 5]$ | $-e + 4$ |
61 | $[61, 61, -w^{2} + 2w + 12]$ | $-\frac{1}{2}e - 8$ |
67 | $[67, 67, -2w^{2} + 6w + 3]$ | $\phantom{-}e + 2$ |
71 | $[71, 71, w^{2} - w - 11]$ | $-\frac{7}{2}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{2} - 3w - 2]$ | $-1$ |