Base field 3.3.564.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[19, 19, -w^{2} + w + 1]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 3x^{3} - 4x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $\phantom{-}e^{3} + 2e^{2} - 2e - 3$ |
3 | $[3, 3, w - 2]$ | $-e^{2} - e + 1$ |
13 | $[13, 13, w^{2} - 2w - 2]$ | $\phantom{-}2e^{3} + 3e^{2} - 4e - 1$ |
17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}e^{3} + 2e^{2} + e - 2$ |
19 | $[19, 19, -w^{2} + w + 1]$ | $-1$ |
31 | $[31, 31, -w + 4]$ | $\phantom{-}3e^{2} + 3e - 5$ |
41 | $[41, 41, -w^{2} + 2w - 2]$ | $-9e^{3} - 19e^{2} + 9e + 15$ |
41 | $[41, 41, -2w^{2} - 3w + 4]$ | $-3e^{3} - 4e^{2} + 6e - 1$ |
41 | $[41, 41, 2w + 1]$ | $-e^{3} - 2e^{2} - 2e - 2$ |
43 | $[43, 43, -w^{2} - w + 5]$ | $-3e^{3} - 3e^{2} + 7e + 4$ |
47 | $[47, 47, -w^{2} + 8]$ | $\phantom{-}e^{3} + 5e^{2} + 4e - 8$ |
47 | $[47, 47, 2w^{2} - w - 8]$ | $-2e^{3} - 4e^{2} + 7e + 6$ |
53 | $[53, 53, w^{2} + w - 7]$ | $-3e^{3} - 2e^{2} + 11e + 1$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $\phantom{-}6e^{3} + 9e^{2} - 14e - 15$ |
61 | $[61, 61, -3w^{2} + 14]$ | $\phantom{-}6e^{3} + 9e^{2} - 7e - 1$ |
61 | $[61, 61, 4w^{2} - 2w - 19]$ | $-6e^{3} - 17e^{2} + 3e + 15$ |
61 | $[61, 61, -2w^{2} + 7]$ | $-7e^{3} - 13e^{2} + 14e + 17$ |
67 | $[67, 67, -2w^{2} - w + 8]$ | $-5e^{3} - 12e^{2} + e + 7$ |
71 | $[71, 71, w^{2} + 2w - 4]$ | $-4e^{2} - 8e + 7$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19, 19, -w^{2} + w + 1]$ | $1$ |