Base field 4.4.16609.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} - x + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[5, 5, w^{2} - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} - 12x - 7\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + w + 4]$ | $\phantom{-}e$ |
3 | $[3, 3, -w^{2} + w + 3]$ | $-e^{3} - 2e^{2} + 3e + 4$ |
5 | $[5, 5, w^{2} - 4]$ | $\phantom{-}1$ |
8 | $[8, 2, w^{3} - w^{2} - 4w + 5]$ | $\phantom{-}2e^{3} + 3e^{2} - 8e - 6$ |
17 | $[17, 17, -w^{2} + w + 5]$ | $-3e^{3} - 4e^{2} + 11e + 4$ |
27 | $[27, 3, -w^{3} + 4w - 2]$ | $\phantom{-}2e^{2} - 8$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $-e^{3} - 4e^{2} + e + 6$ |
29 | $[29, 29, -w^{3} + 4w + 2]$ | $\phantom{-}2e^{3} + 4e^{2} - 6e - 12$ |
37 | $[37, 37, -2w^{3} + 3w^{2} + 9w - 13]$ | $-2e^{3} - 4e^{2} + 10e + 12$ |
41 | $[41, 41, w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}2e^{3} + 4e^{2} - 6e - 10$ |
43 | $[43, 43, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}e^{3} + 2e^{2} + e$ |
61 | $[61, 61, w^{2} - 2w - 2]$ | $\phantom{-}4e^{3} + 4e^{2} - 20e - 6$ |
61 | $[61, 61, 2w^{2} - w - 8]$ | $\phantom{-}e^{3} - 5e - 8$ |
67 | $[67, 67, -4w^{3} + 5w^{2} + 18w - 22]$ | $-4e^{3} - 4e^{2} + 20e + 6$ |
73 | $[73, 73, -w^{2} - 2w + 2]$ | $-3e^{3} - 4e^{2} + 15e + 6$ |
79 | $[79, 79, w^{2} - 2w - 4]$ | $-2e^{3} + 10e + 2$ |
89 | $[89, 89, w^{2} + w - 5]$ | $\phantom{-}4e^{3} + 8e^{2} - 12e - 20$ |
89 | $[89, 89, 2w^{3} - 2w^{2} - 9w + 8]$ | $-4e^{3} - 12e^{2} + 8e + 24$ |
89 | $[89, 89, w^{3} - 5w - 5]$ | $\phantom{-}4e^{3} + 6e^{2} - 16e - 18$ |
89 | $[89, 89, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}4e^{3} + 6e^{2} - 16e - 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w^{2} - 4]$ | $-1$ |