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: | $[19,19,-w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $54$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 11x^{4} + 13x^{2} + 4\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e^{5} + 10e^{3} + 3e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
4 | $[4, 2, 2]$ | $-3e^{4} - 31e^{2} - 19$ |
5 | $[5, 5, w + 2]$ | $-e^{5} - 10e^{3} - 4e$ |
7 | $[7, 7, w]$ | $-e^{5} - 10e^{3} - 3e$ |
7 | $[7, 7, w + 6]$ | $\phantom{-}3e^{5} + 31e^{3} + 19e$ |
17 | $[17, 17, w + 8]$ | $-3e^{5} - 31e^{3} - 20e$ |
19 | $[19, 19, w + 1]$ | $-4e^{4} - 41e^{2} - 24$ |
19 | $[19, 19, w - 2]$ | $-1$ |
23 | $[23, 23, w + 9]$ | $-5e^{5} - 51e^{3} - 27e$ |
23 | $[23, 23, w + 13]$ | $\phantom{-}e^{5} + 10e^{3} + 3e$ |
37 | $[37, 37, w + 11]$ | $-10e^{5} - 104e^{3} - 70e$ |
37 | $[37, 37, w + 25]$ | $-7e^{5} - 73e^{3} - 46e$ |
59 | $[59, 59, 3w + 10]$ | $\phantom{-}2e^{4} + 21e^{2} + 24$ |
59 | $[59, 59, 3w - 13]$ | $\phantom{-}5e^{4} + 51e^{2} + 32$ |
73 | $[73, 73, w + 15]$ | $-20e^{5} - 207e^{3} - 126e$ |
73 | $[73, 73, w + 57]$ | $\phantom{-}20e^{5} + 207e^{3} + 126e$ |
89 | $[89, 89, -w - 10]$ | $-2e^{4} - 20e^{2} - 6$ |
89 | $[89, 89, w - 11]$ | $\phantom{-}e^{4} + 9e^{2} - 2$ |
97 | $[97, 97, w + 22]$ | $\phantom{-}6e^{5} + 62e^{3} + 36e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$19$ | $[19,19,-w + 2]$ | $1$ |