# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.85.1-9.1-e Dimension 6 CM no Base change no

# Related objects

• L-function not available

## 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-e Dimension 6 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6} + 26x^{4} + 121x^{2} + 144$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{1}{24}e^{5} + \frac{23}{24}e^{3} + \frac{29}{12}e$
3 $[3, 3, w + 2]$ $-\frac{1}{24}e^{5} - \frac{23}{24}e^{3} - \frac{29}{12}e$
4 $[4, 2, 2]$ $-\frac{3}{16}e^{4} - \frac{71}{16}e^{2} - 10$
5 $[5, 5, w + 2]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, w + 6]$ $-e$
17 $[17, 17, w + 8]$ $\phantom{-}0$
19 $[19, 19, w + 1]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{21}{8}e^{2} + 6$
19 $[19, 19, w - 2]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{21}{8}e^{2} + 6$
23 $[23, 23, w + 9]$ $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{43}{3}e$
23 $[23, 23, w + 13]$ $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{43}{3}e$
37 $[37, 37, w + 11]$ $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{46}{3}e$
37 $[37, 37, w + 25]$ $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{46}{3}e$
59 $[59, 59, 3w + 10]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{29}{8}e^{2} + 14$
59 $[59, 59, 3w - 13]$ $\phantom{-}\frac{1}{8}e^{4} + \frac{29}{8}e^{2} + 14$
73 $[73, 73, w + 15]$ $-\frac{5}{24}e^{5} - \frac{121}{24}e^{3} - \frac{46}{3}e$
73 $[73, 73, w + 57]$ $\phantom{-}\frac{5}{24}e^{5} + \frac{121}{24}e^{3} + \frac{46}{3}e$
89 $[89, 89, -w - 10]$ $\phantom{-}\frac{7}{8}e^{4} + \frac{155}{8}e^{2} + 44$
89 $[89, 89, w - 11]$ $\phantom{-}\frac{7}{8}e^{4} + \frac{155}{8}e^{2} + 44$
97 $[97, 97, w + 22]$ $-\frac{1}{12}e^{5} - \frac{29}{12}e^{3} - \frac{46}{3}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{1}{24}e^{5} - \frac{23}{24}e^{3} - \frac{29}{12}e$
3 $[3, 3, w + 2]$ $\frac{1}{24}e^{5} + \frac{23}{24}e^{3} + \frac{29}{12}e$