Base field 4.4.17428.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 4x + 6\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[3, 3, -w^{2} + w + 3]$ |
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:
\(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 2]$ | $-e - 2$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
3 | $[3, 3, -w^{2} + w + 3]$ | $\phantom{-}1$ |
27 | $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ | $-2e - 7$ |
29 | $[29, 29, w^{3} + w^{2} - 2w - 1]$ | $\phantom{-}e - 8$ |
31 | $[31, 31, -w^{2} - w + 1]$ | $\phantom{-}3e - 1$ |
31 | $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ | $\phantom{-}6e + 5$ |
37 | $[37, 37, -w^{3} + 3w + 1]$ | $-6e + 1$ |
41 | $[41, 41, -w^{2} + w + 5]$ | $-5e - 1$ |
41 | $[41, 41, -w^{3} + w^{2} + 4w - 1]$ | $-e - 4$ |
43 | $[43, 43, -2w - 1]$ | $-5e - 6$ |
47 | $[47, 47, w^{2} + w - 5]$ | $\phantom{-}e - 2$ |
47 | $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ | $\phantom{-}6e + 3$ |
53 | $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ | $-4e - 4$ |
59 | $[59, 59, w^{3} + w^{2} - 4w - 1]$ | $-4e - 11$ |
59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}e - 6$ |
71 | $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ | $-4e + 2$ |
71 | $[71, 71, w^{2} + 3w + 1]$ | $\phantom{-}9e$ |
73 | $[73, 73, w^{3} - 5w + 1]$ | $\phantom{-}6e + 9$ |
89 | $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ | $-e - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w^{2} + w + 3]$ | $-1$ |