Base field 4.4.14336.1
Generator \(w\), with minimal polynomial \(x^{4} - 8x^{2} + 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7,7,w - 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 3x^{3} + 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{3} + w^{2} + 5w - 6]$ | $\phantom{-}e$ |
7 | $[7, 7, w^{3} - w^{2} - 5w + 7]$ | $\phantom{-}e^{3} - 2e^{2} - e + 2$ |
7 | $[7, 7, -w - 1]$ | $-e^{3} + 2e^{2} + 1$ |
7 | $[7, 7, w - 1]$ | $-1$ |
17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}2e^{3} - 5e^{2} - 2e + 8$ |
17 | $[17, 17, w^{2} + w - 5]$ | $-3e^{3} + 4e^{2} + 8e - 3$ |
23 | $[23, 23, -w - 3]$ | $-2e^{3} + e^{2} + 4e + 5$ |
23 | $[23, 23, w - 3]$ | $-4e^{3} + 10e^{2} + 5e - 11$ |
25 | $[25, 5, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}3e^{3} - 5e^{2} - 4e + 7$ |
25 | $[25, 5, -w^{3} - w^{2} + 4w + 3]$ | $-6e^{3} + 14e^{2} + 4e - 11$ |
41 | $[41, 41, w^{3} - 4w - 1]$ | $\phantom{-}5e^{3} - 12e^{2} - 3e + 13$ |
41 | $[41, 41, -w^{3} + 4w - 1]$ | $-3e^{3} + 7e^{2} + 7e - 8$ |
71 | $[71, 71, -w^{3} + 2w^{2} + 4w - 9]$ | $\phantom{-}8e^{3} - 10e^{2} - 19e + 9$ |
71 | $[71, 71, w^{3} + 2w^{2} - 4w - 9]$ | $\phantom{-}e + 6$ |
73 | $[73, 73, w^{3} - w^{2} - 5w + 3]$ | $-5e^{3} + 4e^{2} + 16e - 4$ |
73 | $[73, 73, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}5e^{3} - 4e^{2} - 13e + 3$ |
79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}5e^{3} - 8e^{2} - 8e + 12$ |
79 | $[79, 79, -2w^{3} + 8w + 5]$ | $\phantom{-}3e^{3} - 9e^{2} + 2e + 11$ |
81 | $[81, 3, -3]$ | $\phantom{-}e^{3} - 8e^{2} + 3e + 8$ |
89 | $[89, 89, -w^{3} - 2w^{2} + 6w + 13]$ | $\phantom{-}6e^{3} - 8e^{2} - 17e + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7,7,w - 1]$ | $1$ |