# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 9 Level $[9, 3, 3]$ Label 2.2.85.1-9.1-d Dimension 4 CM no Base change yes

# 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-d Dimension 4 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:
$$x^{4}$$ $$\mathstrut -\mathstrut 6x^{3}$$ $$\mathstrut +\mathstrut 6x^{2}$$ $$\mathstrut +\mathstrut 11x$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}1$
3 $[3, 3, w + 2]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}e$
5 $[5, 5, w + 2]$ $-e^{3} + 4e^{2} - 5$
7 $[7, 7, w]$ $\phantom{-}e^{2} - 3e - 2$
7 $[7, 7, w + 6]$ $\phantom{-}e^{2} - 3e - 2$
17 $[17, 17, w + 8]$ $-2e^{2} + 6e + 2$
19 $[19, 19, w + 1]$ $\phantom{-}e^{3} - 5e^{2} + 3e + 5$
19 $[19, 19, w - 2]$ $\phantom{-}e^{3} - 5e^{2} + 3e + 5$
23 $[23, 23, w + 9]$ $\phantom{-}e^{3} - 4e^{2} - 2e + 9$
23 $[23, 23, w + 13]$ $\phantom{-}e^{3} - 4e^{2} - 2e + 9$
37 $[37, 37, w + 11]$ $\phantom{-}e^{2} - 5e + 2$
37 $[37, 37, w + 25]$ $\phantom{-}e^{2} - 5e + 2$
59 $[59, 59, 3w + 10]$ $-2e^{3} + 6e^{2} + 4e - 4$
59 $[59, 59, 3w - 13]$ $-2e^{3} + 6e^{2} + 4e - 4$
73 $[73, 73, w + 15]$ $-3e^{2} + 7e + 6$
73 $[73, 73, w + 57]$ $-3e^{2} + 7e + 6$
89 $[89, 89, -w - 10]$ $-2e^{3} + 8e^{2} + 2e - 14$
89 $[89, 89, w - 11]$ $-2e^{3} + 8e^{2} + 2e - 14$
97 $[97, 97, w + 22]$ $\phantom{-}2e^{3} - 8e^{2} + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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