Base field 4.4.6224.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 5\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[26, 26, -w^{3} + 2w^{2} + 4w - 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - x^{2} - 5x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - w^{2} - 4w + 2]$ | $-1$ |
5 | $[5, 5, w]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{3} + w^{2} + 3w - 2]$ | $\phantom{-}2e^{2} - 4e - 6$ |
13 | $[13, 13, -w^{3} + 4w + 2]$ | $-1$ |
19 | $[19, 19, w^{3} - w^{2} - 5w + 2]$ | $-e^{2} + 2$ |
29 | $[29, 29, -w^{2} - w + 3]$ | $-e^{2} + e + 5$ |
29 | $[29, 29, w^{2} - w - 1]$ | $-2e^{2} + 5e + 6$ |
37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}e^{2} + 2e - 6$ |
37 | $[37, 37, -w^{3} + 5w + 1]$ | $\phantom{-}3e^{2} - 5e - 9$ |
41 | $[41, 41, -w^{3} + 2w^{2} + 3w - 7]$ | $\phantom{-}4e^{2} - 5e - 13$ |
47 | $[47, 47, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}2e^{2} - 5e - 5$ |
47 | $[47, 47, 2w^{3} - 3w^{2} - 8w + 6]$ | $\phantom{-}3e^{2} - 6e - 5$ |
59 | $[59, 59, -2w^{3} + w^{2} + 7w - 3]$ | $-e^{2} + 4$ |
67 | $[67, 67, w^{3} - 2w^{2} - 3w + 1]$ | $\phantom{-}e^{2} + e + 3$ |
73 | $[73, 73, -2w - 1]$ | $-6e^{2} + 10e + 20$ |
79 | $[79, 79, 2w^{2} - 2w - 9]$ | $\phantom{-}e^{2} - 2e - 9$ |
81 | $[81, 3, -3]$ | $\phantom{-}2e^{2} - 6e + 2$ |
97 | $[97, 97, -3w + 2]$ | $\phantom{-}4e^{2} - 6e - 12$ |
101 | $[101, 101, w^{3} - 3w^{2} - w + 4]$ | $-5e^{2} + 15e + 15$ |
101 | $[101, 101, 2w^{3} - w^{2} - 9w + 1]$ | $\phantom{-}3e^{2} - e - 5$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{3} - w^{2} - 4w + 2]$ | $1$ |
$13$ | $[13, 13, -w^{3} + 4w + 2]$ | $1$ |