# Properties

 Base field 4.4.10512.1 Weight [2, 2, 2, 2] Level norm 1 Level $[1, 1, 1]$ Label 4.4.10512.1-1.1-a Dimension 4 CM yes 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 $[1, 1, 1]$ Label 4.4.10512.1-1.1-a Dimension 4 Is CM yes Is base change yes Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 13x^{2}$$ $$\mathstrut +\mathstrut 24$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}e$
9 $[9, 3, w^{3} - w^{2} - 5w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
11 $[11, 11, -w^{3} + w^{2} + 6w + 2]$ $\phantom{-}0$
11 $[11, 11, w - 1]$ $\phantom{-}0$
13 $[13, 13, w^{3} - 2w^{2} - 4w + 2]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e$
23 $[23, 23, w^{2} - 2w - 2]$ $\phantom{-}0$
23 $[23, 23, w^{3} - w^{2} - 6w - 3]$ $\phantom{-}0$
23 $[23, 23, -w^{2} + 2w + 5]$ $\phantom{-}0$
23 $[23, 23, -w + 2]$ $\phantom{-}0$
37 $[37, 37, 2w^{3} - 2w^{2} - 12w - 1]$ $-2e^{2} + 16$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e$
37 $[37, 37, w^{3} - 2w^{2} - 5w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{17}{2}e$
37 $[37, 37, -w^{3} + w^{2} + 6w - 2]$ $-2e^{2} + 16$
47 $[47, 47, w^{2} - 2w - 1]$ $\phantom{-}0$
47 $[47, 47, w^{2} - 2w - 6]$ $\phantom{-}0$
59 $[59, 59, 2w - 1]$ $\phantom{-}0$
59 $[59, 59, -2w^{3} + 2w^{2} + 12w + 3]$ $\phantom{-}0$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}4e^{2} - 26$
83 $[83, 83, -w^{3} + w^{2} + 4w + 3]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.