# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 12 Level $[12,6,-2w + 2]$ Label 2.2.85.1-12.2-e Dimension 4 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 $[12,6,-2w + 2]$ Label 2.2.85.1-12.2-e Dimension 4 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:
$$x^{4}$$ $$\mathstrut +\mathstrut 12x^{2}$$ $$\mathstrut +\mathstrut 16$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
3 $[3, 3, w + 2]$ $-\frac{1}{8}e^{3} - e$
4 $[4, 2, 2]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}e$
7 $[7, 7, w]$ $-e$
7 $[7, 7, w + 6]$ $-\frac{1}{2}e^{3} - 5e$
17 $[17, 17, w + 8]$ $-\frac{1}{2}e^{3} - 4e$
19 $[19, 19, w + 1]$ $-e^{2} - 4$
19 $[19, 19, w - 2]$ $\phantom{-}e^{2} + 4$
23 $[23, 23, w + 9]$ $\phantom{-}e$
23 $[23, 23, w + 13]$ $\phantom{-}\frac{1}{2}e^{3} + 5e$
37 $[37, 37, w + 11]$ $\phantom{-}\frac{1}{2}e^{3} + 7e$
37 $[37, 37, w + 25]$ $-\frac{1}{2}e^{3} - 5e$
59 $[59, 59, 3w + 10]$ $\phantom{-}2e^{2} + 12$
59 $[59, 59, 3w - 13]$ $-4$
73 $[73, 73, w + 15]$ $-e^{3} - 10e$
73 $[73, 73, w + 57]$ $-e^{3} - 14e$
89 $[89, 89, -w - 10]$ $-e^{2} - 2$
89 $[89, 89, w - 11]$ $-e^{2} - 18$
97 $[97, 97, w + 22]$ $\phantom{-}\frac{1}{2}e^{3} + 8e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3,3,-w + 1]$ $\frac{1}{8}e^{3} + e$
4 $[4,2,2]$ $-1$