Base field 3.3.785.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 5\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[8, 2, 2]$ |
Dimension: | $4$ |
CM: | no |
Base change: | no |
Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 13x^{2} - 2x + 37\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w - 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w]$ | $\phantom{-}e^{3} - 3e^{2} - 7e + 18$ |
5 | $[5, 5, -w + 3]$ | $\phantom{-}e^{3} - 3e^{2} - 7e + 18$ |
8 | $[8, 2, 2]$ | $\phantom{-}1$ |
9 | $[9, 3, w^{2} + w - 4]$ | $\phantom{-}e^{3} - 3e^{2} - 6e + 18$ |
13 | $[13, 13, w + 3]$ | $\phantom{-}e^{3} - 3e^{2} - 5e + 18$ |
17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 14$ |
23 | $[23, 23, w^{2} - 2]$ | $-3e^{3} + 6e^{2} + 20e - 37$ |
23 | $[23, 23, w^{2} - 3]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
23 | $[23, 23, -w^{2} + 8]$ | $\phantom{-}e^{3} - e^{2} - 7e + 4$ |
29 | $[29, 29, w - 4]$ | $\phantom{-}2e^{3} - 4e^{2} - 14e + 22$ |
37 | $[37, 37, w^{2} + w - 8]$ | $-2e^{3} + 3e^{2} + 13e - 11$ |
41 | $[41, 41, w^{2} + 2w - 4]$ | $\phantom{-}2e^{3} - 4e^{2} - 11e + 22$ |
47 | $[47, 47, 2w^{2} + w - 8]$ | $-2e^{3} + 5e^{2} + 13e - 33$ |
59 | $[59, 59, -2w^{2} - 3w + 6]$ | $\phantom{-}e^{3} - 6e^{2} - 5e + 35$ |
61 | $[61, 61, -2w - 1]$ | $\phantom{-}3e^{3} - 5e^{2} - 19e + 26$ |
67 | $[67, 67, -2w - 3]$ | $-2e^{3} + 6e^{2} + 13e - 29$ |
79 | $[79, 79, 2w^{2} - 9]$ | $-e^{3} + 4e^{2} + 8e - 29$ |
109 | $[109, 109, w^{2} + 2w - 6]$ | $-9e^{3} + 20e^{2} + 62e - 113$ |
109 | $[109, 109, 2w^{2} + w - 14]$ | $\phantom{-}4e^{3} - 11e^{2} - 27e + 61$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$8$ | $[8, 2, 2]$ | $-1$ |