# Properties

 Base field 4.4.10512.1 Weight [2, 2, 2, 2] Level norm 23 Level $[23, 23, w^{2} - 2w - 2]$ Label 4.4.10512.1-23.1-c 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 $[23, 23, w^{2} - 2w - 2]$ Label 4.4.10512.1-23.1-c Dimension 6 Is CM no Is base change no Parent newspace dimension 16

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 16x^{4}$$ $$\mathstrut +\mathstrut 25x^{2}$$ $$\mathstrut -\mathstrut 8$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}e$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $-\frac{1}{10}e^{5} + \frac{6}{5}e^{3} + \frac{23}{10}e$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{29}{5}e^{3} + \frac{9}{5}e$
11 $[11, 11, w - 1]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{17}{5}e^{2} + \frac{12}{5}$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $\phantom{-}\frac{9}{10}e^{5} - \frac{69}{5}e^{3} + \frac{133}{10}e$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{9}{10}e^{5} + \frac{69}{5}e^{3} - \frac{133}{10}e$
23 $[23, 23, w^{2} - 2w - 2]$ $\phantom{-}1$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $-\frac{1}{5}e^{5} + \frac{17}{5}e^{3} - \frac{47}{5}e$
23 $[23, 23, -w^{2} + 2w + 5]$ $-\frac{2}{5}e^{5} + \frac{29}{5}e^{3} - \frac{14}{5}e$
23 $[23, 23, -w + 2]$ $-\frac{2}{5}e^{4} + \frac{29}{5}e^{2} - \frac{44}{5}$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{12}{5}e^{2} - \frac{8}{5}$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $-\frac{3}{10}e^{5} + \frac{23}{5}e^{3} - \frac{61}{10}e$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{7}{10}e^{5} + \frac{52}{5}e^{3} - \frac{49}{10}e$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{4}{5}e^{4} - \frac{63}{5}e^{2} + \frac{28}{5}$
47 $[47, 47, w^{2} - 2w - 1]$ $-e^{4} + 15e^{2} - 16$
47 $[47, 47, w^{2} - 2w - 6]$ $\phantom{-}e^{5} - 15e^{3} + 10e$
59 $[59, 59, 2w - 1]$ $\phantom{-}\frac{4}{5}e^{4} - \frac{58}{5}e^{2} + \frac{8}{5}$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $\phantom{-}\frac{2}{5}e^{5} - \frac{29}{5}e^{3} + \frac{9}{5}e$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-\frac{1}{5}e^{4} + \frac{17}{5}e^{2} - \frac{2}{5}$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $-2e^{4} + 29e^{2} - 20$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
23 $[23, 23, w^{2} - 2w - 2]$ $-1$