Base field 6.6.1134389.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 6x^{3} + 4x^{2} - 3x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[7, 7, w^{2} - w - 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 5x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
7 | $[7, 7, w^{2} - w - 2]$ | $-1$ |
13 | $[13, 13, w^{4} - 2w^{3} - 3w^{2} + 5w]$ | $\phantom{-}e$ |
17 | $[17, 17, -w^{3} + w^{2} + 3w]$ | $\phantom{-}6$ |
19 | $[19, 19, w^{3} - w^{2} - 3w + 1]$ | $-e + 6$ |
19 | $[19, 19, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e - 6$ |
23 | $[23, 23, -w^{4} + 2w^{3} + 3w^{2} - 3w - 2]$ | $\phantom{-}e - 2$ |
31 | $[31, 31, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 1]$ | $\phantom{-}2e - 4$ |
37 | $[37, 37, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ | $\phantom{-}3e - 8$ |
37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 1]$ | $-2e + 6$ |
47 | $[47, 47, -w^{3} + 2w^{2} + w - 3]$ | $-2e + 4$ |
64 | $[64, 2, -2]$ | $-2e + 5$ |
67 | $[67, 67, 2w - 1]$ | $-4e + 12$ |
79 | $[79, 79, w^{4} - w^{3} - 4w^{2} + 2w]$ | $\phantom{-}0$ |
79 | $[79, 79, -w^{5} + 2w^{4} + 3w^{3} - 5w^{2} - w + 4]$ | $-4e + 8$ |
97 | $[97, 97, w^{5} - 2w^{4} - 3w^{3} + 6w^{2} - 3]$ | $\phantom{-}2e - 18$ |
97 | $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 9w^{2} - 2w - 4]$ | $-2e + 10$ |
101 | $[101, 101, w^{5} - 2w^{4} - 3w^{3} + 5w^{2} - w - 2]$ | $-2e + 6$ |
101 | $[101, 101, w^{5} - 3w^{4} - 2w^{3} + 10w^{2} - w - 5]$ | $-2e + 6$ |
103 | $[103, 103, 2w^{5} - 3w^{4} - 9w^{3} + 8w^{2} + 8w - 3]$ | $\phantom{-}e - 2$ |
107 | $[107, 107, w^{2} - 2w - 3]$ | $\phantom{-}e - 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,w^{2}-w-2]$ | $1$ |