Base field 4.4.16317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[7, 7, -w^{2} + 2w + 1]$ |
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:
\(x^{2} - 11\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 2]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + 2w + 1]$ | $-1$ |
7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}3$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}2$ |
16 | $[16, 2, 2]$ | $-3$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ | $-e$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w - 2]$ | $\phantom{-}0$ |
25 | $[25, 5, w^{2} - w - 3]$ | $-2$ |
37 | $[37, 37, 2w - 1]$ | $\phantom{-}7$ |
43 | $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ | $-10$ |
43 | $[43, 43, w^{3} - w^{2} - 3w + 1]$ | $\phantom{-}1$ |
59 | $[59, 59, 2w - 5]$ | $-2e$ |
59 | $[59, 59, -2w - 3]$ | $\phantom{-}2e$ |
79 | $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ | $\phantom{-}11$ |
79 | $[79, 79, -w^{3} + w^{2} + 6w - 2]$ | $-11$ |
83 | $[83, 83, -w^{3} + 7w]$ | $\phantom{-}2e$ |
83 | $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ | $\phantom{-}e$ |
83 | $[83, 83, -w^{3} + w^{2} + 5w - 3]$ | $-2e$ |
83 | $[83, 83, w^{2} - 2w - 6]$ | $\phantom{-}e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{2} + 2w + 1]$ | $1$ |