Base field 4.4.11324.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, -w^{3} + 4w - 2]$ |
Dimension: | $3$ |
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:
\(x^{3} + x^{2} - 8x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
4 | $[4, 2, -w^{3} + 4w + 1]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
13 | $[13, 13, -w^{2} + 3]$ | $-e + 1$ |
17 | $[17, 17, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 2$ |
19 | $[19, 19, -w^{3} + 3w - 1]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 6$ |
23 | $[23, 23, -w + 3]$ | $\phantom{-}e + 1$ |
31 | $[31, 31, -w^{2} - 2w + 1]$ | $-e^{2} + e + 6$ |
41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}2e^{2} - 12$ |
43 | $[43, 43, 2w - 1]$ | $\phantom{-}e^{2} + 4e - 5$ |
53 | $[53, 53, -w - 3]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 10$ |
53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $-e^{2} - e + 14$ |
61 | $[61, 61, w^{3} - 3w - 5]$ | $\phantom{-}e^{2} - e - 4$ |
67 | $[67, 67, w^{3} + w^{2} - 5w - 1]$ | $-\frac{1}{2}e^{2} - \frac{5}{2}e$ |
81 | $[81, 3, -3]$ | $-e^{2} - e + 6$ |
83 | $[83, 83, -w^{3} + 5w - 3]$ | $-3e^{2} - e + 18$ |
89 | $[89, 89, w^{2} + 1]$ | $\phantom{-}\frac{3}{2}e^{2} + \frac{3}{2}e - 8$ |
97 | $[97, 97, w^{3} - w^{2} - 5w + 1]$ | $-e^{2} - 3e$ |
97 | $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ | $-e^{2} - e + 6$ |
97 | $[97, 97, w^{3} - 3w - 3]$ | $-e + 9$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |
$5$ | $[5, 5, w + 1]$ | $-1$ |