Base field 4.4.17428.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 4x + 6\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 4, w^{2} + w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $3$ |
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 | $[2, 2, w - 2]$ | $\phantom{-}1$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}e$ |
27 | $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ | $\phantom{-}2e + 3$ |
29 | $[29, 29, w^{3} + w^{2} - 2w - 1]$ | $\phantom{-}e$ |
31 | $[31, 31, -w^{2} - w + 1]$ | $-e + 2$ |
31 | $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ | $\phantom{-}3$ |
37 | $[37, 37, -w^{3} + 3w + 1]$ | $\phantom{-}3e$ |
41 | $[41, 41, -w^{2} + w + 5]$ | $\phantom{-}e - 6$ |
41 | $[41, 41, -w^{3} + w^{2} + 4w - 1]$ | $-2e + 4$ |
43 | $[43, 43, -2w - 1]$ | $\phantom{-}7$ |
47 | $[47, 47, w^{2} + w - 5]$ | $\phantom{-}e + 5$ |
47 | $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ | $\phantom{-}7e - 1$ |
53 | $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ | $-7e - 3$ |
59 | $[59, 59, w^{3} + w^{2} - 4w - 1]$ | $-5e + 1$ |
59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $-2e + 2$ |
71 | $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ | $-7e + 2$ |
71 | $[71, 71, w^{2} + 3w + 1]$ | $-5e + 5$ |
73 | $[73, 73, w^{3} - 5w + 1]$ | $\phantom{-}6e + 2$ |
89 | $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ | $-4e - 1$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w - 2]$ | $-1$ |
$2$ | $[2, 2, w + 1]$ | $-1$ |