Base field 6.6.1397493.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 3x^{4} + 10x^{3} + 3x^{2} - 6x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[17,17,w^{3} - w^{2} - 4w]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 1]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{2} + 2w + 1]$ | $-2e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $\phantom{-}1$ |
19 | $[19, 19, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + w - 4]$ | $-2e + 4$ |
19 | $[19, 19, w^{2} - w - 1]$ | $-2e - 4$ |
37 | $[37, 37, w^{4} - 2w^{3} - 3w^{2} + 3w + 2]$ | $\phantom{-}2e - 2$ |
37 | $[37, 37, w^{4} - 4w^{3} + w^{2} + 7w - 3]$ | $-e$ |
53 | $[53, 53, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 6]$ | $-3e - 8$ |
53 | $[53, 53, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $-4$ |
64 | $[64, 2, -2]$ | $-6e - 3$ |
71 | $[71, 71, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 3w - 1]$ | $-8e + 2$ |
71 | $[71, 71, 2w^{5} - 5w^{4} - 8w^{3} + 15w^{2} + 12w - 6]$ | $\phantom{-}9e - 9$ |
71 | $[71, 71, 2w^{5} - 6w^{4} - 6w^{3} + 18w^{2} + 9w - 7]$ | $-3e + 9$ |
73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 16w^{2} - 7w + 3]$ | $-5e + 4$ |
73 | $[73, 73, -2w^{5} + 6w^{4} + 5w^{3} - 17w^{2} - 6w + 6]$ | $\phantom{-}9e - 3$ |
89 | $[89, 89, w^{5} - 2w^{4} - 5w^{3} + 6w^{2} + 8w - 4]$ | $\phantom{-}6e - 6$ |
89 | $[89, 89, w^{5} - w^{4} - 9w^{3} + 7w^{2} + 16w - 6]$ | $\phantom{-}3e - 13$ |
89 | $[89, 89, 2w^{5} - 6w^{4} - 4w^{3} + 15w^{2} + 3w - 3]$ | $-4e$ |
89 | $[89, 89, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 10w - 6]$ | $\phantom{-}5e - 13$ |
107 | $[107, 107, w^{5} - 2w^{4} - 7w^{3} + 10w^{2} + 12w - 6]$ | $-e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17,17,w^{3} - w^{2} - 4w]$ | $-1$ |