# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 15 Level $[15, 15, w + 2]$ Label 2.2.85.1-15.1-c Dimension 2 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 $[15, 15, w + 2]$ Label 2.2.85.1-15.1-c Dimension 2 Is CM no Is base change no Parent newspace dimension 30

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 3x$$ $$\mathstrut -\mathstrut 1$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $-1$
7 $[7, 7, w]$ $-e - 2$
7 $[7, 7, w + 6]$ $\phantom{-}e$
17 $[17, 17, w + 8]$ $-2e + 1$
19 $[19, 19, w + 1]$ $-1$
19 $[19, 19, w - 2]$ $-3e - 7$
23 $[23, 23, w + 9]$ $-3e - 3$
23 $[23, 23, w + 13]$ $\phantom{-}2e - 1$
37 $[37, 37, w + 11]$ $-4$
37 $[37, 37, w + 25]$ $\phantom{-}6e + 8$
59 $[59, 59, 3w + 10]$ $-e - 10$
59 $[59, 59, 3w - 13]$ $\phantom{-}3e - 3$
73 $[73, 73, w + 15]$ $\phantom{-}5$
73 $[73, 73, w + 57]$ $\phantom{-}e + 3$
89 $[89, 89, -w - 10]$ $-3e - 6$
89 $[89, 89, w - 11]$ $\phantom{-}6e + 9$
97 $[97, 97, w + 22]$ $\phantom{-}10e + 15$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $-1$
5 $[5, 5, w + 2]$ $1$