Base field 4.4.17609.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 10x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[10, 10, w^{3} - 7w + 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{3} + 6w - 2]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{3} - 7w + 3]$ | $\phantom{-}e + 1$ |
11 | $[11, 11, -w^{3} + 6w - 4]$ | $\phantom{-}2e - 4$ |
17 | $[17, 17, w^{3} + w^{2} - 6w - 1]$ | $-3e + 8$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $-3e + 8$ |
31 | $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ | $-e + 6$ |
37 | $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ | $-4e + 2$ |
41 | $[41, 41, w^{2} + 2w - 4]$ | $-4e + 6$ |
47 | $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ | $-3e + 4$ |
47 | $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ | $-4e + 12$ |
59 | $[59, 59, -2w^{3} + 13w - 6]$ | $\phantom{-}4e - 6$ |
59 | $[59, 59, -w^{3} - w^{2} + 5w + 2]$ | $\phantom{-}5e - 14$ |
59 | $[59, 59, w^{2} + w - 1]$ | $\phantom{-}4e - 6$ |
59 | $[59, 59, w^{2} + 2w - 6]$ | $\phantom{-}4e - 6$ |
61 | $[61, 61, -w^{3} + w^{2} + 8w - 7]$ | $-2e + 10$ |
67 | $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ | $\phantom{-}6e - 14$ |
73 | $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ | $\phantom{-}2e - 10$ |
81 | $[81, 3, -3]$ | $-2e - 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 1]$ | $-1$ |
$5$ | $[5, 5, w^{3} + w^{2} - 4w + 1]$ | $-1$ |