Base field 4.4.19025.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 13x^{2} + 14x + 44\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $35$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 4x^{3} + 2x^{2} - 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{2} - 2w - 6]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} + 7]$ | $-1$ |
5 | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $\phantom{-}1$ |
5 | $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ | $-e^{3} - 3e^{2} + 2$ |
11 | $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ | $\phantom{-}2e^{3} + 6e^{2} - 2e - 6$ |
11 | $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ | $-2e^{2} - 3e + 5$ |
31 | $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ | $-e^{3} - 4e^{2} - 3e + 2$ |
31 | $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ | $\phantom{-}e^{3} + 4e^{2} + 5e - 2$ |
41 | $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ | $\phantom{-}e^{3} + 4e^{2} + 3e - 10$ |
41 | $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ | $-4e^{3} - 11e^{2} + e + 8$ |
41 | $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ | $-4e^{2} - 6e + 6$ |
41 | $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ | $-2e^{3} - 6e^{2} - 4e + 2$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ | $-e^{3} + 5e$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ | $\phantom{-}3e^{3} + 13e^{2} + 9e - 11$ |
71 | $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ | $-4e^{3} - 11e^{2} + 5e + 6$ |
71 | $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ | $\phantom{-}3e^{3} + 13e^{2} + 7e - 13$ |
81 | $[81, 3, -3]$ | $\phantom{-}6$ |
89 | $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ | $\phantom{-}6e^{3} + 17e^{2} + 4e - 1$ |
89 | $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ | $\phantom{-}e^{3} + 6e^{2} + 6e - 3$ |
89 | $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ | $\phantom{-}3e^{3} + 12e^{2} + 5e - 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w^{2} + 7]$ | $1$ |
$5$ | $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ | $-1$ |