# Properties

 Base field 4.4.10512.1 Weight [2, 2, 2, 2] Level norm 13 Level $[13,13,w^{2} - w - 4]$ Label 4.4.10512.1-13.2-a Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.10512.1

Generator $$w$$, with minimal polynomial $$x^{4} - 7x^{2} - 6x + 1$$; narrow class number $$4$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[13,13,w^{2} - w - 4]$ Label 4.4.10512.1-13.2-a Dimension 6 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 55x^{4}$$ $$\mathstrut +\mathstrut 718x^{2}$$ $$\mathstrut -\mathstrut 999$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{615}e^{4} + \frac{37}{615}e^{2} - \frac{676}{205}$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}\frac{8}{615}e^{4} - \frac{319}{615}e^{2} + \frac{127}{205}$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-\frac{1}{123}e^{5} + \frac{15}{41}e^{3} - \frac{350}{123}e$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{615}e^{4} - \frac{37}{615}e^{2} - \frac{349}{205}$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}1$
23 $[23, 23, w^{2} - 2w - 2]$ $-\frac{1}{123}e^{5} + \frac{15}{41}e^{3} - \frac{473}{123}e$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $\phantom{-}\frac{1}{615}e^{5} + \frac{37}{615}e^{3} - \frac{676}{205}e$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}\frac{2}{615}e^{5} - \frac{131}{615}e^{3} + \frac{1274}{615}e$
23 $[23, 23, -w + 2]$ $\phantom{-}\frac{1}{205}e^{5} - \frac{94}{615}e^{3} - \frac{139}{615}e$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $-\frac{26}{615}e^{4} + \frac{883}{615}e^{2} - \frac{874}{205}$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $-\frac{11}{205}e^{4} + \frac{413}{205}e^{2} - \frac{2497}{205}$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}\frac{2}{123}e^{4} - \frac{49}{123}e^{2} - \frac{122}{41}$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{17}{615}e^{4} - \frac{601}{615}e^{2} + \frac{1013}{205}$
47 $[47, 47, w^{2} - 2w - 1]$ $\phantom{-}\frac{11}{615}e^{5} - \frac{206}{205}e^{3} + \frac{7417}{615}e$
47 $[47, 47, w^{2} - 2w - 6]$ $-\frac{1}{615}e^{5} - \frac{37}{615}e^{3} + \frac{471}{205}e$
59 $[59, 59, 2w - 1]$ $\phantom{-}\frac{11}{615}e^{5} - \frac{206}{205}e^{3} + \frac{6802}{615}e$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $-\frac{1}{615}e^{5} - \frac{37}{615}e^{3} + \frac{676}{205}e$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-\frac{9}{205}e^{4} + \frac{282}{205}e^{2} - \frac{1018}{205}$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $\phantom{-}\frac{1}{205}e^{5} - \frac{94}{615}e^{3} + \frac{1091}{615}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13,13,w^{2} - w - 4]$ $-1$