# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 3 Level $[3, 3, w]$ Label 2.2.85.1-3.1-b Dimension 1 CM no Base change no

# 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 $[3, 3, w]$ Label 2.2.85.1-3.1-b Dimension 1 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $-2$
4 $[4, 2, 2]$ $-1$
5 $[5, 5, w + 2]$ $\phantom{-}0$
7 $[7, 7, w]$ $-4$
7 $[7, 7, w + 6]$ $\phantom{-}2$
17 $[17, 17, w + 8]$ $-6$
19 $[19, 19, w + 1]$ $\phantom{-}8$
19 $[19, 19, w - 2]$ $-4$
23 $[23, 23, w + 9]$ $\phantom{-}0$
23 $[23, 23, w + 13]$ $-6$
37 $[37, 37, w + 11]$ $\phantom{-}2$
37 $[37, 37, w + 25]$ $-10$
59 $[59, 59, 3w + 10]$ $\phantom{-}0$
59 $[59, 59, 3w - 13]$ $-12$
73 $[73, 73, w + 15]$ $\phantom{-}8$
73 $[73, 73, w + 57]$ $\phantom{-}8$
89 $[89, 89, -w - 10]$ $\phantom{-}6$
89 $[89, 89, w - 11]$ $-6$
97 $[97, 97, w + 22]$ $-10$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$