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: | $[15, 15, w^{3} - w^{2} - 5w]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 2x - 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}1$ |
5 | $[5, 5, w - 1]$ | $-1$ |
7 | $[7, 7, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}0$ |
11 | $[11, 11, -w^{2} + w + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, -w^{3} + w^{2} + 3w - 1]$ | $-e - 2$ |
16 | $[16, 2, 2]$ | $-3$ |
17 | $[17, 17, -w^{3} + 5w + 2]$ | $-2$ |
29 | $[29, 29, -w^{2} + w + 1]$ | $-e - 2$ |
37 | $[37, 37, -w^{3} + 2w^{2} + 4w - 4]$ | $-2$ |
41 | $[41, 41, -w^{3} + w^{2} + 5w + 1]$ | $-6$ |
41 | $[41, 41, w^{2} - 5]$ | $\phantom{-}2$ |
47 | $[47, 47, w^{3} - w^{2} - 5w - 2]$ | $-4$ |
47 | $[47, 47, -w^{3} + 2w^{2} + 4w - 1]$ | $-4$ |
53 | $[53, 53, w^{3} - 4w - 4]$ | $\phantom{-}e - 2$ |
53 | $[53, 53, 2w^{3} - 2w^{2} - 9w + 1]$ | $-10$ |
61 | $[61, 61, -w^{3} + w^{2} + 6w - 2]$ | $\phantom{-}2e - 2$ |
71 | $[71, 71, w^{3} - w^{2} - 6w - 2]$ | $-2e - 4$ |
103 | $[103, 103, 2w^{3} - 2w^{2} - 8w + 1]$ | $\phantom{-}2e$ |
103 | $[103, 103, -3w^{3} + 3w^{2} + 13w - 5]$ | $-2e$ |
109 | $[109, 109, 2w^{3} - w^{2} - 8w - 4]$ | $\phantom{-}e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $-1$ |
$5$ | $[5, 5, w - 1]$ | $1$ |