Base field 3.3.473.1
Generator \(w\), with minimal polynomial \(x^{3} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[33, 33, -w^{2} + 2w + 3]$ |
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 |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $-\frac{1}{2}e + 3$ |
9 | $[9, 3, -w^{2} + w + 4]$ | $\phantom{-}2$ |
11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}2$ |
11 | $[11, 11, -w^{2} - w + 1]$ | $-1$ |
13 | $[13, 13, w + 3]$ | $-e$ |
17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}e + 2$ |
25 | $[25, 5, w^{2} + w - 4]$ | $-e + 2$ |
37 | $[37, 37, w^{2} + w - 5]$ | $-e - 8$ |
41 | $[41, 41, 2w^{2} + w - 6]$ | $-2e + 2$ |
43 | $[43, 43, w^{2} - 3w - 2]$ | $-3e + 4$ |
43 | $[43, 43, -w + 4]$ | $\phantom{-}e - 4$ |
71 | $[71, 71, w^{2} - 8]$ | $\phantom{-}3e - 4$ |
73 | $[73, 73, 3w + 5]$ | $-e + 2$ |
73 | $[73, 73, w^{2} - 2w - 5]$ | $\phantom{-}3e$ |
73 | $[73, 73, w^{2} - 2w - 7]$ | $\phantom{-}2e - 10$ |
79 | $[79, 79, 2w^{2} + w - 9]$ | $\phantom{-}e - 12$ |
83 | $[83, 83, 3w^{2} - 2w - 13]$ | $\phantom{-}5e$ |
89 | $[89, 89, -w^{2} - 2w + 9]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |
$11$ | $[11, 11, -w^{2} - w + 1]$ | $1$ |