Base field 3.3.1016.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[6, 6, w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}1$ |
2 | $[2, 2, w - 3]$ | $\phantom{-}e$ |
3 | $[3, 3, w^{2} - w - 5]$ | $-1$ |
9 | $[9, 3, w^{2} + w - 1]$ | $\phantom{-}e - 3$ |
13 | $[13, 13, 2w^{2} - 2w - 11]$ | $\phantom{-}e + 1$ |
29 | $[29, 29, -w^{2} - 3w - 1]$ | $-2$ |
29 | $[29, 29, -w^{2} + w + 3]$ | $-e - 1$ |
29 | $[29, 29, 2w - 5]$ | $-4e + 2$ |
31 | $[31, 31, -w^{2} + w + 1]$ | $-4$ |
37 | $[37, 37, -2w - 1]$ | $-2e$ |
43 | $[43, 43, -2w - 3]$ | $\phantom{-}2e - 6$ |
47 | $[47, 47, 2w - 3]$ | $\phantom{-}e + 3$ |
59 | $[59, 59, 4w^{2} + 8w - 1]$ | $-3e - 1$ |
61 | $[61, 61, -w^{2} - w - 1]$ | $-2e$ |
67 | $[67, 67, w^{2} + w - 5]$ | $-4e + 4$ |
71 | $[71, 71, w^{2} - w - 9]$ | $-4e + 4$ |
73 | $[73, 73, -2w^{2} + 2w + 9]$ | $\phantom{-}2e + 4$ |
73 | $[73, 73, 6w^{2} + 10w - 7]$ | $\phantom{-}5e - 7$ |
73 | $[73, 73, 3w^{2} - 3w - 17]$ | $-2e + 12$ |
79 | $[79, 79, -2w^{2} + 2w + 15]$ | $\phantom{-}2e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |
$3$ | $[3, 3, w^{2} - w - 5]$ | $1$ |