Base field 3.3.761.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[24, 6, 2w + 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} + 3x - 1\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w + 1]$ | $\phantom{-}1$ |
7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
8 | $[8, 2, 2]$ | $\phantom{-}1$ |
9 | $[9, 3, -w^{2} + 2w + 4]$ | $-2e - 3$ |
11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}2e + 1$ |
13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}e - 3$ |
19 | $[19, 19, w + 3]$ | $-2e - 3$ |
19 | $[19, 19, -w^{2} + 2w + 5]$ | $-e + 2$ |
19 | $[19, 19, -w^{2} + 3w + 2]$ | $-e - 6$ |
23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}e - 4$ |
23 | $[23, 23, -w^{2} + 2]$ | $-2e - 1$ |
23 | $[23, 23, -w + 4]$ | $-3$ |
31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}e - 2$ |
43 | $[43, 43, w^{2} - 3w - 3]$ | $\phantom{-}4e + 3$ |
49 | $[49, 7, w^{2} - 6]$ | $-3e - 8$ |
53 | $[53, 53, 2w - 5]$ | $-2e + 5$ |
61 | $[61, 61, 2w^{2} - 2w - 9]$ | $-8$ |
71 | $[71, 71, 2w - 3]$ | $-3$ |
73 | $[73, 73, 2w^{2} - 5w - 5]$ | $-4$ |
83 | $[83, 83, w^{2} - w - 9]$ | $\phantom{-}4e + 11$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $-1$ |
$8$ | $[8, 2, 2]$ | $-1$ |