Base field 3.3.257.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 4x + 3\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[35, 35, -w + 4]$ |
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:
\(x^{3} - 2x^{2} - 5x + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 1]$ | $\phantom{-}1$ |
7 | $[7, 7, -w^{2} + 2]$ | $-1$ |
8 | $[8, 2, 2]$ | $-e^{2} + e + 5$ |
9 | $[9, 3, -w^{2} + w + 4]$ | $-e^{2} + 2e + 2$ |
19 | $[19, 19, w^{2} + w - 4]$ | $\phantom{-}e$ |
25 | $[25, 5, -w^{2} + 2w + 2]$ | $-2e + 2$ |
37 | $[37, 37, 2w + 1]$ | $\phantom{-}2e^{2} - 5e - 6$ |
41 | $[41, 41, -2w^{2} - w + 7]$ | $\phantom{-}2e^{2} - 4e - 6$ |
43 | $[43, 43, -2w^{2} + 5]$ | $-e$ |
47 | $[47, 47, 3w - 4]$ | $-e^{2} - 2e + 8$ |
49 | $[49, 7, 2w^{2} - w - 5]$ | $\phantom{-}2e - 6$ |
53 | $[53, 53, -2w^{2} + 2w + 7]$ | $\phantom{-}e^{2} - 10$ |
61 | $[61, 61, -w^{2} - 3w + 4]$ | $-2e + 6$ |
61 | $[61, 61, 3w^{2} - w - 10]$ | $\phantom{-}2e^{2} - 6e - 10$ |
61 | $[61, 61, w^{2} - 2w - 4]$ | $-3e + 10$ |
67 | $[67, 67, 2w^{2} - w - 4]$ | $\phantom{-}e^{2} - 12$ |
67 | $[67, 67, 2w^{2} - w - 2]$ | $\phantom{-}3e^{2} - 4e - 12$ |
67 | $[67, 67, w^{2} + 2w - 5]$ | $\phantom{-}4e^{2} - 4e - 12$ |
71 | $[71, 71, -2w^{2} - w + 10]$ | $-2e^{2} + 8$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5, 5, w + 1]$ | $-1$ |
$7$ | $[7, 7, -w^{2} + 2]$ | $1$ |