Base field 3.3.169.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[65,65,-w^{2} + w + 7]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
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 |
---|---|---|
5 | $[5, 5, -w^{2} + 2w + 3]$ | $-\frac{1}{2}e + 2$ |
5 | $[5, 5, -w^{2} + w + 2]$ | $\phantom{-}1$ |
5 | $[5, 5, -w + 1]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $\phantom{-}\frac{1}{2}e - 1$ |
13 | $[13, 13, -w^{2} + 3]$ | $-1$ |
27 | $[27, 3, 3]$ | $-\frac{3}{2}e + 2$ |
31 | $[31, 31, -2w^{2} + 3w + 3]$ | $\phantom{-}4$ |
31 | $[31, 31, -w^{2} + 5]$ | $-2e + 2$ |
31 | $[31, 31, -w^{2} + 3w + 4]$ | $-2e + 2$ |
47 | $[47, 47, 2w - 3]$ | $-e - 2$ |
47 | $[47, 47, 2w^{2} - 4w - 7]$ | $-\frac{5}{2}e$ |
47 | $[47, 47, 2w^{2} - 2w - 3]$ | $\phantom{-}\frac{1}{2}e - 4$ |
53 | $[53, 53, 3w^{2} - 4w - 8]$ | $\phantom{-}2e$ |
53 | $[53, 53, 4w^{2} - 6w - 11]$ | $-\frac{3}{2}e$ |
53 | $[53, 53, 3w^{2} - 5w - 6]$ | $\phantom{-}3e - 6$ |
73 | $[73, 73, w^{2} - 4w - 4]$ | $-\frac{3}{2}e + 6$ |
73 | $[73, 73, 2w^{2} - w - 8]$ | $\phantom{-}\frac{3}{2}e + 2$ |
73 | $[73, 73, 3w^{2} - 5w - 5]$ | $-e - 4$ |
79 | $[79, 79, -3w^{2} + 5w + 4]$ | $\phantom{-}\frac{5}{2}e + 2$ |
79 | $[79, 79, 2w^{2} - w - 9]$ | $-3e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,w^{2} - w - 2]$ | $-1$ |
$13$ | $[13,13,2w^{2} - 3w - 5]$ | $1$ |