Base field 4.4.19796.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + x + 8\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[4, 2, -w^{2} + 3]$ |
Dimension: | $4$ |
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:
\(x^{4} - 8x^{2} + 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w^{2} + 2]$ | $-\frac{1}{2}e^{2} + 1$ |
2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $\phantom{-}0$ |
5 | $[5, 5, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 3w + 5]$ | $-\frac{1}{2}e^{3} + e$ |
17 | $[17, 17, -w^{2} - w + 3]$ | $\phantom{-}\frac{1}{2}e^{3} - 3e$ |
19 | $[19, 19, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}e^{3} - 8e$ |
23 | $[23, 23, w^{3} - 2w^{2} - 3w + 3]$ | $-2$ |
31 | $[31, 31, -w^{2} + w + 1]$ | $\phantom{-}2e^{3} - 10e$ |
47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $-2e^{3} + 12e$ |
49 | $[49, 7, 2w^{3} - 5w^{2} - 7w + 11]$ | $-e^{3} + 11e$ |
53 | $[53, 53, -3w^{3} + 9w^{2} + 10w - 31]$ | $-12$ |
53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $-e^{2} - 2$ |
61 | $[61, 61, 3w^{3} - 6w^{2} - 13w + 13]$ | $-\frac{3}{2}e^{3} + 7e$ |
61 | $[61, 61, 2w^{2} - 7]$ | $-2e^{3} + 15e$ |
71 | $[71, 71, w^{2} - 3w - 5]$ | $\phantom{-}2e^{2} - 14$ |
73 | $[73, 73, 2w - 3]$ | $-2e^{3} + 9e$ |
73 | $[73, 73, -2w^{3} + 6w^{2} + 6w - 19]$ | $-\frac{1}{2}e^{3} + e$ |
79 | $[79, 79, 2w^{2} - 5]$ | $\phantom{-}2e^{2} - 10$ |
81 | $[81, 3, -3]$ | $-5e^{2} + 18$ |
101 | $[101, 101, 2w^{2} - 4w - 9]$ | $-\frac{3}{2}e^{3} + 11e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w^{3} + 2w^{2} + 4w - 5]$ | $-1$ |