Base field 4.4.4525.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 7x^{2} + 3x + 9\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[45,15,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 4]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 3x^{3} - 5x^{2} + 11x + 10\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
5 | $[5, 5, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{7}{3}w + 4]$ | $\phantom{-}e$ |
5 | $[5, 5, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{1}{3}w + 3]$ | $\phantom{-}1$ |
9 | $[9, 3, -w]$ | $-e^{3} + 2e^{2} + 3e$ |
9 | $[9, 3, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w + 1]$ | $\phantom{-}1$ |
16 | $[16, 2, 2]$ | $\phantom{-}e^{2} - 3e - 1$ |
19 | $[19, 19, \frac{2}{3}w^{3} - \frac{2}{3}w^{2} - \frac{11}{3}w]$ | $-e^{3} + 2e^{2} + 5e - 2$ |
19 | $[19, 19, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{1}{3}w + 1]$ | $\phantom{-}e^{2} - 2e - 4$ |
31 | $[31, 31, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{11}{3}w - 2]$ | $\phantom{-}e^{3} - 8e$ |
31 | $[31, 31, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{5}{3}w + 5]$ | $\phantom{-}e^{3} - 7e - 6$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 6]$ | $-4e^{2} + 6e + 14$ |
41 | $[41, 41, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 3]$ | $\phantom{-}e^{3} - 6e^{2} + 4e + 18$ |
61 | $[61, 61, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} + \frac{2}{3}w + 4]$ | $\phantom{-}3e^{2} - 6e - 10$ |
61 | $[61, 61, \frac{2}{3}w^{3} + \frac{1}{3}w^{2} - \frac{14}{3}w - 2]$ | $-3e^{2} + 4e + 10$ |
71 | $[71, 71, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 7]$ | $\phantom{-}3e^{3} - 8e^{2} - 5e + 14$ |
71 | $[71, 71, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w]$ | $-2e^{2} + 8$ |
89 | $[89, 89, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{10}{3}w - 3]$ | $-2e^{3} + 7e^{2} + 2e - 14$ |
89 | $[89, 89, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $-2e^{2} + 3e + 8$ |
101 | $[101, 101, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{7}{3}w - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 7e$ |
101 | $[101, 101, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + \frac{11}{3}w - 4]$ | $\phantom{-}e^{3} + 2e^{2} - 5e - 20$ |
101 | $[101, 101, \frac{2}{3}w^{3} - \frac{5}{3}w^{2} - \frac{8}{3}w + 3]$ | $-e^{3} - e^{2} + 13e + 4$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{1}{3}w - 3]$ | $-1$ |
$9$ | $[9,3,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $-1$ |