Base field 4.4.16400.1
Generator \(w\), with minimal polynomial \(x^{4} - 13x^{2} + 41\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, w^{2} + w - 7]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 16x^{2} + 20\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ | $\phantom{-}1$ |
5 | $[5, 5, -w - 2]$ | $-1$ |
5 | $[5, 5, -w + 2]$ | $-1$ |
11 | $[11, 11, -2w^{2} - w + 12]$ | $\phantom{-}e$ |
11 | $[11, 11, 2w^{2} - w - 12]$ | $-\frac{1}{4}e^{3} + \frac{7}{2}e$ |
19 | $[19, 19, -w^{2} - w + 4]$ | $\phantom{-}\frac{1}{2}e^{3} - 7e$ |
19 | $[19, 19, w^{2} - w - 4]$ | $\phantom{-}e$ |
29 | $[29, 29, -w - 1]$ | $-\frac{1}{2}e^{2}$ |
29 | $[29, 29, w - 1]$ | $\phantom{-}e^{2} - 10$ |
31 | $[31, 31, -2w^{2} - w + 14]$ | $\phantom{-}\frac{1}{2}e^{3} - 7e$ |
31 | $[31, 31, w^{3} - 3w^{2} - 6w + 19]$ | $-2e$ |
31 | $[31, 31, -w^{3} - 3w^{2} + 6w + 19]$ | $-e$ |
31 | $[31, 31, -2w^{2} + w + 14]$ | $-\frac{1}{4}e^{3} + \frac{5}{2}e$ |
41 | $[41, 41, -w]$ | $-\frac{1}{2}e^{2} + 3$ |
71 | $[71, 71, w^{3} + 3w^{2} - 7w - 19]$ | $-\frac{3}{4}e^{3} + \frac{17}{2}e$ |
71 | $[71, 71, w^{3} - 3w^{2} - 7w + 19]$ | $\phantom{-}\frac{1}{4}e^{3} - \frac{9}{2}e$ |
79 | $[79, 79, w^{3} + 3w^{2} - 9w - 25]$ | $-\frac{1}{4}e^{3} + \frac{1}{2}e$ |
79 | $[79, 79, w^{3} - 3w^{2} - 9w + 25]$ | $-\frac{3}{4}e^{3} + \frac{27}{2}e$ |
81 | $[81, 3, -3]$ | $-\frac{3}{2}e^{2} + 8$ |
89 | $[89, 89, -w^{3} - 4w^{2} + 6w + 24]$ | $-\frac{1}{2}e^{2}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{3} + 2w^{2} + 6w - 11]$ | $-1$ |
$5$ | $[5, 5, -w - 2]$ | $1$ |