Base field 3.3.961.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 8\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[2,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + 3]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + x^{2} - 6x - 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, \frac{1}{2}w^{2} - \frac{1}{2}w - 4]$ | $-\frac{1}{2}e^{2} - \frac{1}{2}e + 2$ |
2 | $[2, 2, \frac{1}{2}w^{2} + \frac{1}{2}w - 3]$ | $\phantom{-}1$ |
2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{2} + w + 7]$ | $\phantom{-}e + 7$ |
23 | $[23, 23, w^{2} + w - 7]$ | $\phantom{-}e^{2} - 2e - 7$ |
23 | $[23, 23, -2w + 1]$ | $\phantom{-}e^{2} + e - 2$ |
27 | $[27, 3, 3]$ | $-e^{2} + 2e + 3$ |
29 | $[29, 29, -w^{2} - 3w + 1]$ | $\phantom{-}e^{2} - 7$ |
29 | $[29, 29, w^{2} - 3w + 1]$ | $-e^{2} - 3e + 6$ |
29 | $[29, 29, -2w^{2} + 21]$ | $-2e^{2} - e + 9$ |
31 | $[31, 31, -3w^{2} + w + 31]$ | $-e^{2} - e + 2$ |
47 | $[47, 47, 2w - 3]$ | $-2e^{2} - 3e + 5$ |
47 | $[47, 47, w^{2} + w - 5]$ | $\phantom{-}2e^{2} - e - 9$ |
47 | $[47, 47, w^{2} - w - 9]$ | $-e^{2} + 3e + 6$ |
61 | $[61, 61, w^{2} - w - 11]$ | $\phantom{-}2e^{2} - 2e - 6$ |
61 | $[61, 61, -w^{2} - w + 3]$ | $-e - 5$ |
61 | $[61, 61, -2w + 5]$ | $\phantom{-}e^{2} - 3e - 8$ |
89 | $[89, 89, w^{2} - w - 1]$ | $\phantom{-}2e^{2} + e - 1$ |
89 | $[89, 89, w^{2} + w - 13]$ | $\phantom{-}2e^{2} - 12$ |
89 | $[89, 89, -2w - 5]$ | $\phantom{-}3e^{2} + 3e - 16$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,-\frac{1}{2}w^{2} - \frac{1}{2}w + 3]$ | $-1$ |