Base field 6.6.966125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ |
Dimension: | $4$ |
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:
\(x^{4} - 4x^{3} + 9x - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}2e^{3} - 5e^{2} - 7e + 10$ |
19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $-e^{3} + 4e^{2} + e - 5$ |
25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $-1$ |
29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $-e^{2} + 4e + 3$ |
31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $-3e^{3} + 9e^{2} + 7e - 11$ |
31 | $[31, 31, -w^{2} + 2]$ | $-e^{3} + e^{2} + 5e$ |
59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $-2e + 7$ |
59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $-e^{2} - e + 11$ |
59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}4e^{3} - 11e^{2} - 15e + 20$ |
61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $-e^{3} + e^{2} + 5e + 4$ |
64 | $[64, 2, 2]$ | $\phantom{-}2e^{3} - 5e^{2} - 11e + 9$ |
71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $-4e^{3} + 11e^{2} + 11e - 20$ |
71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}e^{3} - 3e^{2} + 2e + 4$ |
71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $\phantom{-}3e^{3} - 10e^{2} - 9e + 20$ |
71 | $[71, 71, w^{3} - 5w]$ | $\phantom{-}2e^{3} - 5e^{2} - 7e + 5$ |
79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}e^{3} - 6e^{2} + 5e + 11$ |
89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $-2e^{3} + 6e^{2} + 8e - 15$ |
101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $-2e^{3} + 5e^{2} + 4e + 5$ |
101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $\phantom{-}4e^{3} - 13e^{2} - 9e + 20$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$25$ | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $1$ |