Base field 4.4.11344.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 9, -w^{2} + w + 3]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $\phantom{-}0$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}0$ |
11 | $[11, 11, w + 2]$ | $-4$ |
27 | $[27, 3, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}4e$ |
29 | $[29, 29, -w^{2} + 3w + 1]$ | $-2e$ |
31 | $[31, 31, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}6e$ |
31 | $[31, 31, -w^{2} + 2w + 4]$ | $-6e$ |
47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $-8$ |
49 | $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ | $-6e$ |
49 | $[49, 7, w^{3} - w^{2} - 3w - 2]$ | $-4e$ |
53 | $[53, 53, w^{3} - 3w^{2} - w + 2]$ | $\phantom{-}6$ |
53 | $[53, 53, w^{3} - 5w - 5]$ | $\phantom{-}4e$ |
61 | $[61, 61, 2w - 1]$ | $\phantom{-}6e$ |
61 | $[61, 61, -w^{3} + 4w^{2} - 4]$ | $-10$ |
67 | $[67, 67, 3w^{3} - 3w^{2} - 13w - 4]$ | $-8e$ |
73 | $[73, 73, -w^{3} + 4w^{2} - 10]$ | $-2e$ |
73 | $[73, 73, w^{2} - w + 1]$ | $-6$ |
83 | $[83, 83, -4w^{3} + 5w^{2} + 17w + 1]$ | $-12$ |
83 | $[83, 83, 3w^{3} - 3w^{2} - 14w - 5]$ | $-4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $-1$ |