Base field 3.3.1101.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 12\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[12, 6, w^{2} + w - 9]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 2x^{3} - 4x^{2} - 4x + 3\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
3 | $[3, 3, -w + 3]$ | $\phantom{-}1$ |
3 | $[3, 3, w - 1]$ | $\phantom{-}e^{2} + e - 3$ |
4 | $[4, 2, w^{2} + w - 7]$ | $-1$ |
19 | $[19, 19, w + 1]$ | $-2e^{3} - 3e^{2} + 6e + 3$ |
23 | $[23, 23, w^{2} - 2w - 1]$ | $-e^{3} + 5e - 4$ |
31 | $[31, 31, -2w^{2} + 19]$ | $\phantom{-}2e^{3} + 5e^{2} - 6e - 4$ |
31 | $[31, 31, -w^{2} + 5]$ | $\phantom{-}3e^{3} + 7e^{2} - 6e - 9$ |
31 | $[31, 31, -3w + 5]$ | $\phantom{-}2e + 1$ |
41 | $[41, 41, w^{2} + 2w - 7]$ | $\phantom{-}e^{3} + 4e^{2} + e - 4$ |
43 | $[43, 43, w^{2} - 11]$ | $-3e^{3} - 6e^{2} + 9e + 7$ |
47 | $[47, 47, 3w - 7]$ | $-3e^{3} - 4e^{2} + 11e + 7$ |
53 | $[53, 53, -3w^{2} - 6w + 11]$ | $-2e^{3} - 4e^{2} + 5e + 4$ |
59 | $[59, 59, 2w - 1]$ | $-e^{3} - 2e^{2} + 2e - 6$ |
67 | $[67, 67, 2w^{2} + w - 19]$ | $-e^{3} + 2e^{2} + 9e$ |
67 | $[67, 67, 3w^{2} + 2w - 25]$ | $\phantom{-}e^{3} + 8e^{2} + 5e - 16$ |
67 | $[67, 67, w - 5]$ | $-2e^{3} - 4e^{2} + 9e + 6$ |
73 | $[73, 73, -4w^{2} - 3w + 29]$ | $\phantom{-}2e^{3} + e^{2} - 8e + 5$ |
73 | $[73, 73, 2w^{2} - w - 11]$ | $\phantom{-}e^{3} + 3e^{2} + e - 8$ |
73 | $[73, 73, w^{2} + 2w - 11]$ | $-2e^{2} + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, -w + 3]$ | $-1$ |
$4$ | $[4, 2, w^{2} + w - 7]$ | $1$ |