Properties

Base field \(\Q(\sqrt{85}) \)
Weight [2, 2]
Level norm 9
Level $[9, 3, 3]$
Label 2.2.85.1-9.1-a
Dimension 2
CM no
Base change yes

Related objects

Downloads

Learn more about

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 $[9, 3, 3]$
Label 2.2.85.1-9.1-a
Dimension 2
Is CM no
Is base change yes
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} \) \(\mathstrut +\mathstrut 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{1}{3}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{3}e$
4 $[4, 2, 2]$ $\phantom{-}0$
5 $[5, 5, w + 2]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}\frac{2}{3}e$
7 $[7, 7, w + 6]$ $\phantom{-}\frac{2}{3}e$
17 $[17, 17, w + 8]$ $\phantom{-}\frac{2}{3}e$
19 $[19, 19, w + 1]$ $\phantom{-}5$
19 $[19, 19, w - 2]$ $\phantom{-}5$
23 $[23, 23, w + 9]$ $-\frac{1}{3}e$
23 $[23, 23, w + 13]$ $-\frac{1}{3}e$
37 $[37, 37, w + 11]$ $\phantom{-}\frac{2}{3}e$
37 $[37, 37, w + 25]$ $\phantom{-}\frac{2}{3}e$
59 $[59, 59, 3w + 10]$ $\phantom{-}0$
59 $[59, 59, 3w - 13]$ $\phantom{-}0$
73 $[73, 73, w + 15]$ $-2e$
73 $[73, 73, w + 57]$ $-2e$
89 $[89, 89, -w - 10]$ $-10$
89 $[89, 89, w - 11]$ $-10$
97 $[97, 97, w + 22]$ $-\frac{8}{3}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{1}{3}e$
3 $[3, 3, w + 2]$ $-\frac{1}{3}e$