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: | $[4, 2, -w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 2x^{3} - 5x^{2} + 10x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
4 | $[4, 2, -w + 1]$ | $-1$ |
5 | $[5, 5, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 4]$ | $-e^{3} + e^{2} + 6e - 4$ |
5 | $[5, 5, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 10w - 4]$ | $-e^{3} + e^{2} + 6e - 4$ |
25 | $[25, 5, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 4]$ | $\phantom{-}2e^{2} + 2e - 8$ |
37 | $[37, 37, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + 4w]$ | $-3e^{3} + e^{2} + 16e - 8$ |
37 | $[37, 37, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w]$ | $-3e^{3} + e^{2} + 16e - 8$ |
43 | $[43, 43, -\frac{3}{2}w^{3} + \frac{1}{2}w^{2} + 10w - 2]$ | $\phantom{-}3e^{3} - 2e^{2} - 15e + 6$ |
43 | $[43, 43, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + 10w + 2]$ | $\phantom{-}3e^{3} - 2e^{2} - 15e + 6$ |
49 | $[49, 7, -w^{2} - w + 3]$ | $\phantom{-}e^{2} - e - 6$ |
49 | $[49, 7, -w^{2} + w + 3]$ | $\phantom{-}e^{2} - e - 6$ |
59 | $[59, 59, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 6$ |
59 | $[59, 59, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 2]$ | $\phantom{-}e^{3} - 2e^{2} - 5e + 6$ |
61 | $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 3w + 2]$ | $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$ |
61 | $[61, 61, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 8w - 4]$ | $\phantom{-}2e^{3} - 2e^{2} - 10e + 6$ |
73 | $[73, 73, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 2w]$ | $\phantom{-}4e^{3} - e^{2} - 19e + 2$ |
73 | $[73, 73, w^{2} - w + 1]$ | $-2e^{3} + e^{2} + 9e + 2$ |
73 | $[73, 73, w^{2} + w + 1]$ | $-2e^{3} + e^{2} + 9e + 2$ |
73 | $[73, 73, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 2w]$ | $\phantom{-}4e^{3} - e^{2} - 19e + 2$ |
81 | $[81, 3, -3]$ | $-2e^{3} + 4e^{2} + 12e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$4$ | $[4, 2, -w + 1]$ | $1$ |