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: | $[12,6,-2w + 2]$ |
Dimension: | $6$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} + 12x^{4} + 32x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{8}e^{5} + \frac{5}{4}e^{3} + 2e$ |
4 | $[4, 2, 2]$ | $-1$ |
5 | $[5, 5, w + 2]$ | $-\frac{3}{8}e^{5} - 4e^{3} - 6e$ |
7 | $[7, 7, w]$ | $-\frac{1}{8}e^{5} - 2e^{3} - 7e$ |
7 | $[7, 7, w + 6]$ | $-\frac{1}{8}e^{5} - \frac{3}{2}e^{3} - 4e$ |
17 | $[17, 17, w + 8]$ | $-\frac{1}{2}e^{5} - 5e^{3} - 9e$ |
19 | $[19, 19, w + 1]$ | $\phantom{-}\frac{3}{4}e^{4} + 7e^{2} + 10$ |
19 | $[19, 19, w - 2]$ | $-\frac{3}{4}e^{4} - 6e^{2} - 4$ |
23 | $[23, 23, w + 9]$ | $-\frac{1}{8}e^{5} - \frac{3}{2}e^{3} - e$ |
23 | $[23, 23, w + 13]$ | $\phantom{-}\frac{5}{8}e^{5} + \frac{13}{2}e^{3} + 10e$ |
37 | $[37, 37, w + 11]$ | $-\frac{9}{8}e^{5} - 12e^{3} - 21e$ |
37 | $[37, 37, w + 25]$ | $\phantom{-}\frac{1}{8}e^{5} + \frac{5}{2}e^{3} + 11e$ |
59 | $[59, 59, 3w + 10]$ | $-e^{4} - 9e^{2} - 8$ |
59 | $[59, 59, 3w - 13]$ | $-e^{4} - 9e^{2} - 8$ |
73 | $[73, 73, w + 15]$ | $\phantom{-}\frac{1}{2}e^{5} + 7e^{3} + 20e$ |
73 | $[73, 73, w + 57]$ | $-\frac{3}{4}e^{5} - 8e^{3} - 10e$ |
89 | $[89, 89, -w - 10]$ | $\phantom{-}\frac{1}{4}e^{4} + 3e^{2} + 4$ |
89 | $[89, 89, w - 11]$ | $\phantom{-}\frac{1}{4}e^{4} + 3e^{2} + 4$ |
97 | $[97, 97, w + 22]$ | $\phantom{-}\frac{3}{4}e^{5} + 9e^{3} + 25e$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,-w + 1]$ | $-\frac{1}{8}e^{5} - \frac{5}{4}e^{3} - 2e$ |
$4$ | $[4,2,2]$ | $1$ |