Base field 4.4.8069.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7, 7, -w^{3} + 4w - 1]$ |
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:
\(x^{2} - x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w^{3} - 4w]$ | $-2$ |
7 | $[7, 7, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{3} + 4w - 1]$ | $\phantom{-}1$ |
13 | $[13, 13, -w^{2} + 3]$ | $-e - 2$ |
16 | $[16, 2, 2]$ | $\phantom{-}1$ |
17 | $[17, 17, w^{3} + w^{2} - 4w - 2]$ | $-6$ |
17 | $[17, 17, -w^{3} + 5w - 2]$ | $-2e + 2$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}e - 4$ |
19 | $[19, 19, -w^{2} - w + 1]$ | $\phantom{-}e - 4$ |
29 | $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ | $-e - 2$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w - 3]$ | $-4e + 2$ |
43 | $[43, 43, w^{3} - w^{2} - 4w + 2]$ | $-3e + 4$ |
43 | $[43, 43, w^{3} - 6w]$ | $\phantom{-}2e - 4$ |
47 | $[47, 47, -w^{3} - w^{2} + 5w]$ | $\phantom{-}e - 8$ |
49 | $[49, 7, w^{2} + 2w - 2]$ | $-2e + 2$ |
59 | $[59, 59, 2w^{3} - 8w + 3]$ | $-4$ |
67 | $[67, 67, w^{2} - w - 4]$ | $\phantom{-}3e - 4$ |
79 | $[79, 79, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2e$ |
81 | $[81, 3, -3]$ | $-2e + 2$ |
97 | $[97, 97, w^{3} + w^{2} - 5w + 1]$ | $\phantom{-}3e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{3} + 4w - 1]$ | $-1$ |