Base field 4.4.9909.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[17, 17, -w^{3} + 5w + 2]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 6x - 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
5 | $[5, 5, w - 1]$ | $-3$ |
7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e - 1$ |
11 | $[11, 11, -w^{2} + w + 2]$ | $-3$ |
13 | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ | $-e^{2} + e + 5$ |
16 | $[16, 2, 2]$ | $-e^{2} - 2e + 5$ |
17 | $[17, 17, -w^{3} + 5w + 2]$ | $\phantom{-}1$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $\phantom{-}3e$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}e - 4$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w + 1]$ | $-3$ |
41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}e^{2} - 3e - 9$ |
47 | $[47, 47, w^{3} - w^{2} - 5w - 2]$ | $-e^{2} + 3$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ | $-3e^{2} - 3e + 12$ |
53 | $[53, 53, w^{3} - 4w - 4]$ | $-2e^{2} - 3e + 9$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ | $\phantom{-}3e^{2} - 15$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $-1$ |
71 | $[71, 71, w^{3} - w^{2} - 6w - 2]$ | $-3$ |
103 | $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}2e^{2} - 2e - 16$ |
103 | $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ | $-5e + 5$ |
109 | $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ | $-3e^{2} - 2e + 14$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{3} + 5w + 2]$ | $-1$ |