Base field 4.4.7168.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 7\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9,3,w^{2} - w - 1]$ |
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:
\(x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, w]$ | $-e + 1$ |
9 | $[9, 3, w^{2} + w - 1]$ | $\phantom{-}e + 2$ |
9 | $[9, 3, w^{2} - w - 1]$ | $-1$ |
17 | $[17, 17, -w^{3} + 3w - 1]$ | $\phantom{-}3$ |
17 | $[17, 17, w^{3} - 3w - 1]$ | $\phantom{-}3$ |
23 | $[23, 23, -w^{3} - w^{2} + 3w + 4]$ | $-1$ |
23 | $[23, 23, w^{3} - w^{2} - 3w + 4]$ | $-1$ |
41 | $[41, 41, w^{3} - w^{2} - 2w + 3]$ | $-7e + 8$ |
41 | $[41, 41, -w^{3} - w^{2} + 2w + 3]$ | $\phantom{-}5e - 3$ |
49 | $[49, 7, w^{2} - 6]$ | $\phantom{-}4e - 7$ |
71 | $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ | $-2e + 8$ |
71 | $[71, 71, -2w^{2} - 2w + 1]$ | $\phantom{-}10e - 3$ |
73 | $[73, 73, w^{2} - 2w - 2]$ | $-13e + 8$ |
73 | $[73, 73, w^{2} + 2w - 2]$ | $\phantom{-}9$ |
79 | $[79, 79, w^{3} - w^{2} - 5w + 2]$ | $-4e - 3$ |
79 | $[79, 79, -w^{3} - w^{2} + 5w + 2]$ | $-3e + 9$ |
89 | $[89, 89, 2w - 1]$ | $-3e - 1$ |
89 | $[89, 89, -2w - 1]$ | $\phantom{-}10e$ |
97 | $[97, 97, -w^{3} + w^{2} + 4w - 1]$ | $-3e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9,3,w^{2} - w - 1]$ | $1$ |