Base field 4.4.10025.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 10x + 20\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, -w^{3} - 2w^{2} + 7w + 10]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + x^{3} - 11x^{2} + x + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, -w + 2]$ | $\phantom{-}1$ |
4 | $[4, 2, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 4]$ | $\phantom{-}e$ |
5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{5}{2}w + 3]$ | $\phantom{-}e + 1$ |
19 | $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{9}{2}w - 3]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 1$ |
19 | $[19, 19, w - 1]$ | $-e^{3} - 3e^{2} + 5e + 9$ |
31 | $[31, 31, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{7}{2}w - 6]$ | $-e^{2} - 2e + 5$ |
31 | $[31, 31, -w^{3} - 2w^{2} + 7w + 13]$ | $\phantom{-}e^{3} + 3e^{2} - 7e - 9$ |
49 | $[49, 7, -2w^{3} - 2w^{2} + 15w + 9]$ | $-2e^{3} - 6e^{2} + 12e + 18$ |
49 | $[49, 7, \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - \frac{9}{2}w - 4]$ | $\phantom{-}e^{3} + 3e^{2} - 3e - 11$ |
59 | $[59, 59, -\frac{3}{2}w^{3} - \frac{3}{2}w^{2} + \frac{17}{2}w + 8]$ | $-2e^{2} - 4e + 6$ |
59 | $[59, 59, -\frac{1}{2}w^{3} - \frac{5}{2}w^{2} + \frac{11}{2}w + 9]$ | $-e^{3} - 4e^{2} + 5e + 12$ |
61 | $[61, 61, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{9}{2}w + 9]$ | $\phantom{-}0$ |
61 | $[61, 61, -\frac{3}{2}w^{3} - \frac{5}{2}w^{2} + \frac{23}{2}w + 12]$ | $-e^{3} - 4e^{2} + 5e + 14$ |
71 | $[71, 71, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{23}{2}w - 1]$ | $\phantom{-}e^{3} + 4e^{2} - 4e - 9$ |
71 | $[71, 71, \frac{3}{2}w^{3} + \frac{3}{2}w^{2} - \frac{19}{2}w - 9]$ | $\phantom{-}e^{3} + 2e^{2} - 9e + 4$ |
79 | $[79, 79, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{11}{2}w + 4]$ | $\phantom{-}e^{2} - e - 2$ |
79 | $[79, 79, -\frac{5}{2}w^{3} - \frac{7}{2}w^{2} + \frac{37}{2}w + 18]$ | $\phantom{-}4e - 2$ |
81 | $[81, 3, -3]$ | $-e^{3} - 3e^{2} + 4e + 14$ |
89 | $[89, 89, w^{3} - 7w + 1]$ | $\phantom{-}e^{2} + 2e - 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w + 2]$ | $-1$ |
$5$ | $[5, 5, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + \frac{7}{2}w + 10]$ | $-1$ |