Base field 4.4.13448.1
Generator \(w\), with minimal polynomial \(x^{4} - 7x^{2} + 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[20, 10, w^{3} - 6w - 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $23$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 4x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -w + 1]$ | $\phantom{-}1$ |
5 | $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ | $\phantom{-}e^{2} - 4$ |
5 | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $-1$ |
25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ | $\phantom{-}3e^{2} + 2e - 4$ |
37 | $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ | $-6e^{2} - 4e + 14$ |
37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ | $\phantom{-}e^{2} + 2e$ |
43 | $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ | $\phantom{-}2e^{2} + 3e - 6$ |
43 | $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ | $\phantom{-}2e^{2} + 5e - 10$ |
49 | $[49, 7, -w^{2} - w + 3]$ | $-4e^{2} - 7e + 10$ |
49 | $[49, 7, -w^{2} + w + 3]$ | $-e^{2} - e$ |
59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ | $\phantom{-}e^{2} + e - 12$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ | $-3e^{2} - 7e + 10$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ | $-4e^{2} - 2e + 10$ |
61 | $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ | $-2e^{2} - 2e - 2$ |
73 | $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ | $\phantom{-}2e^{2} + e - 6$ |
73 | $[73, 73, w^{2} - w + 1]$ | $-5e$ |
73 | $[73, 73, w^{2} + w + 1]$ | $\phantom{-}3e^{2} + 9e - 8$ |
73 | $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ | $-e^{2} - 5e - 4$ |
81 | $[81, 3, -3]$ | $-2e^{2} - 2e + 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w + 1]$ | $-1$ |
$5$ | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $1$ |