Base field 3.3.1229.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x + 6\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[16, 4, 2w^{2} + 4w - 4]$ |
Dimension: | $3$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} + 2x^{2} - 5x - 9\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{2} + 2w - 2]$ | $\phantom{-}0$ |
3 | $[3, 3, -w + 3]$ | $\phantom{-}e$ |
4 | $[4, 2, -w^{2} + w + 5]$ | $-1$ |
9 | $[9, 3, w^{2} + 2w - 1]$ | $\phantom{-}e^{2} - e - 4$ |
11 | $[11, 11, w + 1]$ | $\phantom{-}e^{2} - 1$ |
13 | $[13, 13, -2w^{2} - 3w + 5]$ | $-2e^{2} + e + 9$ |
17 | $[17, 17, -2w + 5]$ | $-e^{2} + e + 4$ |
19 | $[19, 19, -w^{2} + 5]$ | $\phantom{-}e^{2} - 1$ |
23 | $[23, 23, -w^{2} + 2w + 1]$ | $\phantom{-}3e^{2} + e - 10$ |
29 | $[29, 29, 3w^{2} + 6w - 5]$ | $-e^{2} + e + 9$ |
37 | $[37, 37, 4w^{2} - 2w - 25]$ | $\phantom{-}e^{2} + 2e + 2$ |
67 | $[67, 67, 2w^{2} + 2w - 7]$ | $\phantom{-}0$ |
67 | $[67, 67, -2w^{2} - 5w + 1]$ | $-6e^{2} - 2e + 27$ |
67 | $[67, 67, 2w^{2} + 3w - 7]$ | $-4e^{2} + e + 23$ |
71 | $[71, 71, w - 5]$ | $-7e^{2} - e + 30$ |
73 | $[73, 73, w^{2} + 2w - 5]$ | $\phantom{-}e^{2} + 3e - 5$ |
73 | $[73, 73, 2w^{2} - w - 11]$ | $\phantom{-}e^{2} - 2e - 7$ |
73 | $[73, 73, -2w - 1]$ | $-2e^{2} - 3e + 7$ |
83 | $[83, 83, 4w^{2} - 31]$ | $-3e^{2} + 2e + 15$ |
97 | $[97, 97, 2w^{2} + 2w - 5]$ | $-4e^{2} + 29$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{2} + 2w - 2]$ | $-1$ |
$4$ | $[4, 2, -w^{2} + w + 5]$ | $1$ |