Base field \(\Q(\sqrt{85}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 21\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $4$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} - 6x^{3} + 6x^{2} + 11x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $\phantom{-}e$ |
5 | $[5, 5, w + 2]$ | $-e^{3} + 4e^{2} - 5$ |
7 | $[7, 7, w]$ | $\phantom{-}e^{2} - 3e - 2$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}e^{2} - 3e - 2$ |
17 | $[17, 17, w + 8]$ | $-2e^{2} + 6e + 2$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}e^{3} - 5e^{2} + 3e + 5$ |
19 | $[19, 19, w - 2]$ | $\phantom{-}e^{3} - 5e^{2} + 3e + 5$ |
23 | $[23, 23, w + 9]$ | $\phantom{-}e^{3} - 4e^{2} - 2e + 9$ |
23 | $[23, 23, w + 13]$ | $\phantom{-}e^{3} - 4e^{2} - 2e + 9$ |
37 | $[37, 37, w + 11]$ | $\phantom{-}e^{2} - 5e + 2$ |
37 | $[37, 37, w + 25]$ | $\phantom{-}e^{2} - 5e + 2$ |
59 | $[59, 59, 3w + 10]$ | $-2e^{3} + 6e^{2} + 4e - 4$ |
59 | $[59, 59, 3w - 13]$ | $-2e^{3} + 6e^{2} + 4e - 4$ |
73 | $[73, 73, w + 15]$ | $-3e^{2} + 7e + 6$ |
73 | $[73, 73, w + 57]$ | $-3e^{2} + 7e + 6$ |
89 | $[89, 89, -w - 10]$ | $-2e^{3} + 8e^{2} + 2e - 14$ |
89 | $[89, 89, w - 11]$ | $-2e^{3} + 8e^{2} + 2e - 14$ |
97 | $[97, 97, w + 22]$ | $\phantom{-}2e^{3} - 8e^{2} + 12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w]$ | $-1$ |
$3$ | $[3, 3, w + 2]$ | $-1$ |