Base field 6.6.1081856.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - 2x^{3} + 7x^{2} + 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ |
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:
\(x^{2} + 5x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w^{4} - w^{3} - 4w^{2} + w + 1]$ | $\phantom{-}e$ |
8 | $[8, 2, w^{5} - w^{4} - 5w^{3} + 2w^{2} + 5w]$ | $\phantom{-}2e + 5$ |
17 | $[17, 17, -w^{2} + w + 2]$ | $-4$ |
23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $\phantom{-}1$ |
25 | $[25, 5, -w^{3} + w^{2} + 4w]$ | $-2e - 4$ |
31 | $[31, 31, -w^{3} + 4w + 1]$ | $-4e - 12$ |
31 | $[31, 31, w^{5} - 6w^{3} - w^{2} + 5w]$ | $-3e - 5$ |
41 | $[41, 41, -w^{5} + w^{4} + 5w^{3} - 2w^{2} - 6w - 1]$ | $\phantom{-}2e + 6$ |
47 | $[47, 47, -w^{5} + w^{4} + 6w^{3} - 4w^{2} - 8w + 2]$ | $-2e - 12$ |
49 | $[49, 7, -w^{5} - w^{4} + 7w^{3} + 6w^{2} - 8w - 3]$ | $-4e - 10$ |
71 | $[71, 71, -w^{4} + 5w^{2} + w - 3]$ | $\phantom{-}4e + 6$ |
71 | $[71, 71, w^{4} - 5w^{2} - 2w + 4]$ | $\phantom{-}2e + 2$ |
73 | $[73, 73, -2w^{5} + w^{4} + 10w^{3} - 9w - 1]$ | $\phantom{-}3e + 7$ |
73 | $[73, 73, -w^{5} + 6w^{3} + 2w^{2} - 5w - 1]$ | $-5e - 19$ |
79 | $[79, 79, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 3]$ | $-7e - 17$ |
89 | $[89, 89, w^{5} - 7w^{3} - w^{2} + 9w]$ | $\phantom{-}7e + 15$ |
97 | $[97, 97, 2w^{5} - 2w^{4} - 10w^{3} + 5w^{2} + 10w - 1]$ | $-7e - 16$ |
103 | $[103, 103, w^{5} - w^{4} - 4w^{3} + w^{2} + 3w + 2]$ | $\phantom{-}6e + 14$ |
103 | $[103, 103, -2w^{5} + w^{4} + 11w^{3} - w^{2} - 11w - 1]$ | $-6e - 14$ |
103 | $[103, 103, -w^{4} + 2w^{3} + 4w^{2} - 5w - 2]$ | $\phantom{-}2e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$23$ | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 4w - 1]$ | $-1$ |