Base field 4.4.8957.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + x + 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[9, 3, w^{3} - w^{2} - 4w + 1]$ |
Dimension: | $3$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} - 3x^{2} - 20x + 28\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w^{3} + w^{2} + 5w]$ | $\phantom{-}1$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $\phantom{-}e$ |
13 | $[13, 13, -2w^{3} + w^{2} + 11w + 3]$ | $-e + 2$ |
13 | $[13, 13, w^{3} - 2w^{2} - 4w + 3]$ | $-e + 2$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 6$ |
23 | $[23, 23, -w^{2} + 2]$ | $\phantom{-}2$ |
23 | $[23, 23, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}2$ |
49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}e - 4$ |
49 | $[49, 7, 2w^{3} - 2w^{2} - 9w - 1]$ | $\phantom{-}e - 4$ |
53 | $[53, 53, w^{3} - 3w^{2} + 3]$ | $\phantom{-}e$ |
53 | $[53, 53, 2w^{3} - w^{2} - 8w - 3]$ | $\phantom{-}e$ |
53 | $[53, 53, -w^{3} + w^{2} + 6w - 1]$ | $-e^{2} + e + 12$ |
61 | $[61, 61, -w - 3]$ | $-e^{2} + 2e + 10$ |
61 | $[61, 61, -w^{3} + w^{2} + 5w - 4]$ | $-e^{2} + 2e + 10$ |
79 | $[79, 79, w^{3} - 2w^{2} - 4w + 1]$ | $\phantom{-}2e - 6$ |
79 | $[79, 79, w^{2} - 5]$ | $\phantom{-}2e - 6$ |
101 | $[101, 101, w^{3} - 6w]$ | $-3e$ |
101 | $[101, 101, w^{2} - 2w - 4]$ | $-3e$ |
103 | $[103, 103, 4w^{3} - 3w^{2} - 20w - 3]$ | $-2e - 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w^{3} + w^{2} + 5w]$ | $-1$ |
$3$ | $[3, 3, w - 1]$ | $-1$ |