# Properties

 Base field $$\Q(\sqrt{85})$$ Weight [2, 2] Level norm 7 Level $[7, 7, w]$ Label 2.2.85.1-7.1-b Dimension 5 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 $[7, 7, w]$ Label 2.2.85.1-7.1-b Dimension 5 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:
$$x^{5}$$ $$\mathstrut +\mathstrut 2x^{4}$$ $$\mathstrut -\mathstrut 12x^{3}$$ $$\mathstrut -\mathstrut 13x^{2}$$ $$\mathstrut +\mathstrut 37x$$ $$\mathstrut -\mathstrut 16$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e^{3} - 9e + 4$
3 $[3, 3, w + 2]$ $\phantom{-}e$
4 $[4, 2, 2]$ $-e^{4} - 3e^{3} + 10e^{2} + 23e - 23$
5 $[5, 5, w + 2]$ $\phantom{-}2e^{3} - e^{2} - 18e + 14$
7 $[7, 7, w]$ $\phantom{-}1$
7 $[7, 7, w + 6]$ $\phantom{-}e^{4} + e^{3} - 10e^{2} - 6e + 12$
17 $[17, 17, w + 8]$ $-2e^{3} + e^{2} + 18e - 18$
19 $[19, 19, w + 1]$ $\phantom{-}3e^{4} + 6e^{3} - 28e^{2} - 41e + 44$
19 $[19, 19, w - 2]$ $-2e^{3} + e^{2} + 17e - 20$
23 $[23, 23, w + 9]$ $\phantom{-}2e^{4} - 17e^{2} + 8e$
23 $[23, 23, w + 13]$ $-2e^{3} + 16e - 12$
37 $[37, 37, w + 11]$ $-e^{4} + e^{3} + 9e^{2} - 11e + 2$
37 $[37, 37, w + 25]$ $-3e^{4} - 8e^{3} + 28e^{2} + 56e - 54$
59 $[59, 59, 3w + 10]$ $\phantom{-}5e^{3} - e^{2} - 42e + 28$
59 $[59, 59, 3w - 13]$ $\phantom{-}e^{4} + 4e^{3} - 11e^{2} - 33e + 36$
73 $[73, 73, w + 15]$ $-2e^{3} + e^{2} + 20e - 14$
73 $[73, 73, w + 57]$ $\phantom{-}e^{4} - 9e^{2} + 4e - 6$
89 $[89, 89, -w - 10]$ $-4e^{4} - 9e^{3} + 38e^{2} + 63e - 70$
89 $[89, 89, w - 11]$ $-5e^{4} - 3e^{3} + 46e^{2} + 10e - 30$
97 $[97, 97, w + 22]$ $\phantom{-}11e^{3} - 3e^{2} - 95e + 70$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w]$ $-1$