Base field 4.4.11661.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, -w^{2} + w + 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - x^{3} - 11x^{2} + 4x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $-1$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, w - 1]$ | $-1$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{2} - e - 3$ |
23 | $[23, 23, -w^{3} + 4w + 1]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
25 | $[25, 5, w^{3} - 2w^{2} - 2w + 2]$ | $\phantom{-}e^{2} - 6$ |
25 | $[25, 5, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}e^{2} - 6$ |
29 | $[29, 29, w^{3} - 2w^{2} - 4w + 4]$ | $-2e - 2$ |
29 | $[29, 29, w^{3} - w^{2} - 5w + 1]$ | $-2e - 2$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 3w - 2]$ | $-e^{3} + e^{2} + 8e - 4$ |
43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $-e^{3} + e^{2} + 8e - 4$ |
61 | $[61, 61, -w^{2} + 2w + 4]$ | $-e^{3} + e^{2} + 8e - 2$ |
61 | $[61, 61, w^{2} - 5]$ | $-e^{3} + e^{2} + 8e - 2$ |
79 | $[79, 79, 3w^{3} - 7w^{2} - 8w + 16]$ | $-e^{2} + 8$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 4]$ | $-e^{2} + 8$ |
101 | $[101, 101, -w^{3} + 3w^{2} + w - 7]$ | $\phantom{-}6$ |
101 | $[101, 101, w^{3} - 4w - 4]$ | $\phantom{-}6$ |
103 | $[103, 103, 2w^{3} - w^{2} - 8w - 1]$ | $-3e^{2} + 2e + 16$ |
103 | $[103, 103, 2w^{3} - 5w^{2} - 4w + 8]$ | $-3e^{2} + 2e + 16$ |
107 | $[107, 107, 2w^{2} - 3w - 4]$ | $-2e^{2} + 4e + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $1$ |
$3$ | $[3, 3, w - 1]$ | $1$ |