Base field 3.3.568.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[4, 4, -w^{2} + 2w + 3]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
5 | $[5, 5, w^{2} - w - 7]$ | $-e$ |
11 | $[11, 11, -w^{2} + w + 1]$ | $-2e + 4$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $-3e + 4$ |
25 | $[25, 5, -w^{2} - w - 1]$ | $-3e$ |
27 | $[27, 3, 3]$ | $\phantom{-}2e$ |
29 | $[29, 29, -w^{2} + 3w - 1]$ | $\phantom{-}e - 4$ |
37 | $[37, 37, 3w^{2} - 5w - 13]$ | $\phantom{-}e - 8$ |
41 | $[41, 41, 2w - 1]$ | $-e$ |
53 | $[53, 53, 5w^{2} - 9w - 21]$ | $-2e + 4$ |
53 | $[53, 53, 3w^{2} - 5w - 15]$ | $\phantom{-}4e + 2$ |
53 | $[53, 53, w^{2} - 3w - 7]$ | $-2e + 8$ |
59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}4e - 4$ |
61 | $[61, 61, 2w^{2} - 4w - 9]$ | $\phantom{-}3e - 12$ |
61 | $[61, 61, 2w - 7]$ | $-2e - 8$ |
61 | $[61, 61, 2w - 5]$ | $\phantom{-}3e + 4$ |
67 | $[67, 67, -w^{2} + w - 1]$ | $\phantom{-}2e - 4$ |
71 | $[71, 71, -2w - 5]$ | $-6e + 4$ |
71 | $[71, 71, 3w^{2} - 3w - 19]$ | $\phantom{-}6e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w + 1]$ | $-1$ |