# Properties

 Base field 4.4.4752.1 Weight [2, 2, 2, 2] Level norm 36 Level $[36, 6, -w^{3} + w^{2} + 5w]$ Label 4.4.4752.1-36.1-e Dimension 2 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.4752.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 3x^{2} + 4x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[36, 6, -w^{3} + w^{2} + 5w]$ Label 4.4.4752.1-36.1-e Dimension 2 Is CM no Is base change yes Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 8$$
Norm Prime Eigenvalue
3 $[3, 3, -w - 1]$ $\phantom{-}0$
4 $[4, 2, -w^{3} + w^{2} + 3w]$ $-1$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}e$
13 $[13, 13, w^{3} - 2w^{2} - w + 1]$ $\phantom{-}2$
13 $[13, 13, w^{3} - w^{2} - 2w + 1]$ $\phantom{-}2$
23 $[23, 23, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{5}{2}e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}\frac{5}{2}e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}\frac{3}{2}e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}\frac{3}{2}e$
59 $[59, 59, w^{2} - 5]$ $-\frac{3}{2}e$
59 $[59, 59, w^{2} - 2w - 4]$ $-\frac{3}{2}e$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}10$
61 $[61, 61, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}10$
71 $[71, 71, w^{3} - w^{2} - 2w - 2]$ $-\frac{7}{2}e$
71 $[71, 71, -w^{3} + 2w^{2} + w - 4]$ $-\frac{7}{2}e$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}4$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 6]$ $\phantom{-}4$
83 $[83, 83, -2w^{3} + 3w^{2} + 6w - 6]$ $-\frac{11}{2}e$
83 $[83, 83, -2w^{3} + 4w^{2} + 5w - 5]$ $\phantom{-}e$
83 $[83, 83, -2w^{3} + 2w^{2} + 7w - 2]$ $\phantom{-}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 1]$ $1$
4 $[4, 2, -w^{3} + w^{2} + 3w]$ $1$