Base field 4.4.2624.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 3x^{2} + 2x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[49, 49, w^{3} - 3w^{2} + 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 4x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
4 | $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ | $\phantom{-}2$ |
7 | $[7, 7, -w^{3} + 3w^{2} + w - 3]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{2} + w + 2]$ | $\phantom{-}0$ |
17 | $[17, 17, -w^{3} + 3w^{2} - 3]$ | $-2e + 6$ |
17 | $[17, 17, -w^{3} + w^{2} + 4w]$ | $-\frac{3}{2}e + 1$ |
25 | $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ | $-e + 6$ |
25 | $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ | $\phantom{-}\frac{1}{2}e + 5$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ | $-\frac{1}{2}e - 3$ |
47 | $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ | $\phantom{-}2e - 8$ |
47 | $[47, 47, 2w^{3} - 4w^{2} - 5w]$ | $\phantom{-}3e - 4$ |
49 | $[49, 7, w^{2} - 4w - 1]$ | $-\frac{3}{2}e - 3$ |
71 | $[71, 71, 2w - 3]$ | $-e - 4$ |
71 | $[71, 71, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}e - 10$ |
73 | $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ | $\phantom{-}\frac{1}{2}e - 1$ |
73 | $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ | $\phantom{-}4$ |
73 | $[73, 73, -w^{3} + 3w^{2} - 5]$ | $-\frac{9}{2}e + 11$ |
73 | $[73, 73, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}\frac{5}{2}e - 3$ |
79 | $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ | $-4$ |
79 | $[79, 79, 2w^{3} - 3w^{2} - 5w]$ | $\phantom{-}3e - 6$ |
81 | $[81, 3, -3]$ | $\phantom{-}\frac{1}{2}e - 9$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$7$ | $[7, 7, -w^{2} + w + 2]$ | $1$ |