# Properties

 Base field 4.4.10512.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9, 3, w^{3} - w^{2} - 5w - 1]$ Label 4.4.10512.1-9.1-a Dimension 4 CM no Base change yes

# 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 $[9, 3, w^{3} - w^{2} - 5w - 1]$ Label 4.4.10512.1-9.1-a Dimension 4 Is CM no Is base change yes Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 28x^{2} + 71$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{10}e^{2} + \frac{11}{10}$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $-1$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{10}e^{2} + \frac{29}{10}$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1}{10}e^{2} + \frac{29}{10}$
23 $[23, 23, w^{2} - 2w - 2]$ $-\frac{1}{10}e^{3} + \frac{9}{10}e$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $-\frac{1}{5}e^{3} + \frac{24}{5}e$
23 $[23, 23, -w^{2} + 2w + 5]$ $-\frac{1}{10}e^{3} + \frac{9}{10}e$
23 $[23, 23, -w + 2]$ $-\frac{1}{5}e^{3} + \frac{24}{5}e$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $-\frac{1}{5}e^{2} + \frac{4}{5}$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $-\frac{1}{10}e^{2} + \frac{69}{10}$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $-\frac{1}{10}e^{2} + \frac{69}{10}$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $-\frac{1}{5}e^{2} + \frac{4}{5}$
47 $[47, 47, w^{2} - 2w - 1]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{77}{10}e$
47 $[47, 47, w^{2} - 2w - 6]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{77}{10}e$
59 $[59, 59, 2w - 1]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{67}{10}e$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{67}{10}e$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-\frac{7}{5}e^{2} + \frac{93}{5}$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{29}{5}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $1$