# Properties

 Base field 4.4.4752.1 Weight [2, 2, 2, 2] Level norm 13 Level $[13, 13, w^{3} - 2w^{2} - w + 1]$ Label 4.4.4752.1-13.1-a Dimension 4 CM no Base change no

# 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 $[13, 13, w^{3} - 2w^{2} - w + 1]$ Label 4.4.4752.1-13.1-a Dimension 4 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 12x^{2} + 34$$
Norm Prime Eigenvalue
3 $[3, 3, -w - 1]$ $\phantom{-}e$
4 $[4, 2, -w^{3} + w^{2} + 3w]$ $-e^{2} + 7$
11 $[11, 11, -w^{2} + 3]$ $\phantom{-}e^{3} - 6e$
13 $[13, 13, w^{3} - 2w^{2} - w + 1]$ $-1$
13 $[13, 13, w^{3} - w^{2} - 2w + 1]$ $-3e^{2} + 20$
23 $[23, 23, -w^{3} + w^{2} + 4w - 2]$ $-e$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 2]$ $\phantom{-}2e^{3} - 12e$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ $-e^{3} + 7e$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $\phantom{-}2e^{3} - 13e$
59 $[59, 59, w^{2} - 5]$ $-e^{3} + 3e$
59 $[59, 59, w^{2} - 2w - 4]$ $-e^{3} + 10e$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}2e^{2} - 12$
61 $[61, 61, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}2e^{2} - 12$
71 $[71, 71, w^{3} - w^{2} - 2w - 2]$ $-3e^{3} + 17e$
71 $[71, 71, -w^{3} + 2w^{2} + w - 4]$ $\phantom{-}4e$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}6e^{2} - 36$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 6]$ $\phantom{-}6e^{2} - 36$
83 $[83, 83, -2w^{3} + 3w^{2} + 6w - 6]$ $\phantom{-}e^{3} - 9e$
83 $[83, 83, -2w^{3} + 4w^{2} + 5w - 5]$ $-e^{3} + 2e$
83 $[83, 83, -2w^{3} + 2w^{2} + 7w - 2]$ $-5e^{3} + 31e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
13 $[13, 13, w^{3} - 2w^{2} - w + 1]$ $1$