Base field 3.3.756.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[19, 19, -w^{2} - w + 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 10x + 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w + 3]$ | $-e$ |
7 | $[7, 7, w - 1]$ | $-e - 1$ |
11 | $[11, 11, -w - 3]$ | $\phantom{-}e - 2$ |
13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}0$ |
19 | $[19, 19, -w^{2} - w + 1]$ | $-1$ |
23 | $[23, 23, -w^{2} + 3]$ | $-e^{2} + e + 5$ |
29 | $[29, 29, 2w + 3]$ | $-e^{2} - e + 8$ |
31 | $[31, 31, 2w^{2} - 2w - 9]$ | $-e - 3$ |
53 | $[53, 53, -w^{2} - 1]$ | $-2e^{2} + 9$ |
61 | $[61, 61, 2w - 3]$ | $\phantom{-}e^{2} - 2e - 14$ |
67 | $[67, 67, w^{2} - 2w - 5]$ | $-e^{2} - 4e + 10$ |
67 | $[67, 67, -w^{2} + w + 9]$ | $\phantom{-}e^{2} - e - 11$ |
67 | $[67, 67, -w^{2} + 3w + 3]$ | $\phantom{-}2e^{2} + e - 14$ |
71 | $[71, 71, w^{2} + w - 7]$ | $\phantom{-}e^{2} + e - 9$ |
73 | $[73, 73, -2w^{2} + 3w + 7]$ | $-e^{2} + 2e + 3$ |
89 | $[89, 89, w^{2} - 2w - 7]$ | $-e^{2} - 2e + 5$ |
89 | $[89, 89, -2w^{2} + 1]$ | $-e^{2} - e + 10$ |
89 | $[89, 89, -3w^{2} + 19]$ | $\phantom{-}e^{2} + 2e - 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{2} - w + 1]$ | $1$ |