Base field 3.3.733.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 8\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[22, 22, -w^{2} + 2w + 2]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 3x - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 2]$ | $-1$ |
4 | $[4, 2, -w^{2} - w + 5]$ | $\phantom{-}e$ |
5 | $[5, 5, -w + 3]$ | $\phantom{-}e - 3$ |
7 | $[7, 7, -w^{2} - 2w + 3]$ | $\phantom{-}e + 1$ |
11 | $[11, 11, -w^{2} + 5]$ | $\phantom{-}1$ |
13 | $[13, 13, w + 1]$ | $-2$ |
23 | $[23, 23, w^{2} - 3]$ | $-3e + 3$ |
25 | $[25, 5, w^{2} + 2w - 1]$ | $-2e$ |
27 | $[27, 3, -3]$ | $\phantom{-}e - 5$ |
29 | $[29, 29, -3w + 7]$ | $\phantom{-}2e - 2$ |
43 | $[43, 43, -3w^{2} - 2w + 17]$ | $\phantom{-}2e + 4$ |
49 | $[49, 7, -2w^{2} + w + 11]$ | $-2e + 8$ |
67 | $[67, 67, -2w^{2} - 4w + 3]$ | $-12$ |
71 | $[71, 71, -2w^{2} + w + 9]$ | $\phantom{-}2e$ |
73 | $[73, 73, w^{2} + 2w - 7]$ | $-5e + 13$ |
73 | $[73, 73, -2w^{2} - 2w + 11]$ | $-2e + 4$ |
73 | $[73, 73, w - 5]$ | $\phantom{-}4e - 6$ |
89 | $[89, 89, 2w^{2} + w - 9]$ | $\phantom{-}e - 5$ |
89 | $[89, 89, -w^{2} - 2w + 9]$ | $\phantom{-}2e - 10$ |
89 | $[89, 89, -2w - 1]$ | $-2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 2]$ | $1$ |
$11$ | $[11, 11, -w^{2} + 5]$ | $-1$ |