Base field 4.4.8468.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 4\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[22, 22, -w^{3} + w^{2} + 3w - 2]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} - x^{4} - 9x^{3} + 9x^{2} + 12x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 4w - 2]$ | $\phantom{-}1$ |
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
11 | $[11, 11, -w^{3} + 5w + 1]$ | $\phantom{-}1$ |
17 | $[17, 17, -w^{3} + 3w + 1]$ | $\phantom{-}2e - 2$ |
23 | $[23, 23, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}e^{4} - 9e^{2} + 10$ |
29 | $[29, 29, -w^{3} + w^{2} + 2w - 1]$ | $-e^{4} + 7e^{2} - 2e - 2$ |
29 | $[29, 29, w^{3} + w^{2} - 6w - 5]$ | $-e^{4} + 7e^{2} - 2e - 2$ |
29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e^{4} - 9e^{2} + 2e + 10$ |
47 | $[47, 47, w^{3} - 3w - 3]$ | $-e^{4} + 7e^{2} - 4$ |
53 | $[53, 53, 2w^{2} - 2w - 5]$ | $-2e^{3} + 12e + 2$ |
53 | $[53, 53, -w^{3} + 2w^{2} + 5w - 7]$ | $-2e + 4$ |
59 | $[59, 59, 2w^{3} - 8w - 3]$ | $-e^{4} + 9e^{2} - 10$ |
59 | $[59, 59, w^{3} - w^{2} - 2w + 3]$ | $-2e^{2} + 8$ |
67 | $[67, 67, 2w - 1]$ | $\phantom{-}2e^{4} - 14e^{2} + 2e + 12$ |
71 | $[71, 71, 2w^{2} - 5]$ | $-2e^{3} + 14e$ |
73 | $[73, 73, -w^{3} + w^{2} + 4w + 1]$ | $-2e^{3} + 12e - 6$ |
73 | $[73, 73, -2w^{3} + 8w + 1]$ | $-2e - 4$ |
73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}2e^{3} - 12e$ |
79 | $[79, 79, w^{2} - w + 1]$ | $\phantom{-}2e^{2} - 8$ |
79 | $[79, 79, w^{3} + w^{2} - 4w - 7]$ | $-e^{4} + 7e^{2} - 4e - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{3} - 4w - 2]$ | $-1$ |
$11$ | $[11, 11, -w^{3} + 5w + 1]$ | $-1$ |