# Properties

 Base field 4.4.4752.1 Weight [2, 2, 2, 2] Level norm 39 Level $[39, 39, w^{2} - 2w - 3]$ Label 4.4.4752.1-39.1-d Dimension 1 CM no Base change no

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## 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 $[39, 39, w^{2} - 2w - 3]$ Label 4.4.4752.1-39.1-d Dimension 1 Is CM no Is base change no Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w - 1]$ $-1$
4 $[4, 2, -w^{3} + w^{2} + 3w]$ $-2$
11 $[11, 11, -w^{2} + 3]$ $-6$
13 $[13, 13, w^{3} - 2w^{2} - w + 1]$ $\phantom{-}4$
13 $[13, 13, w^{3} - w^{2} - 2w + 1]$ $\phantom{-}1$
23 $[23, 23, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}4$
23 $[23, 23, w^{3} - 2w^{2} - 3w + 2]$ $-4$
47 $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ $-8$
47 $[47, 47, -w^{3} + w^{2} + 4w - 3]$ $-2$
59 $[59, 59, w^{2} - 5]$ $\phantom{-}4$
59 $[59, 59, w^{2} - 2w - 4]$ $-4$
61 $[61, 61, -w^{3} + 2w^{2} + 4w - 4]$ $-2$
61 $[61, 61, w^{3} - w^{2} - 5w + 1]$ $\phantom{-}4$
71 $[71, 71, w^{3} - w^{2} - 2w - 2]$ $-6$
71 $[71, 71, -w^{3} + 2w^{2} + w - 4]$ $\phantom{-}12$
73 $[73, 73, 2w^{2} - w - 5]$ $-6$
73 $[73, 73, w^{3} - 2w^{2} - 2w + 6]$ $-6$
83 $[83, 83, -2w^{3} + 3w^{2} + 6w - 6]$ $\phantom{-}6$
83 $[83, 83, -2w^{3} + 4w^{2} + 5w - 5]$ $\phantom{-}6$
83 $[83, 83, -2w^{3} + 2w^{2} + 7w - 2]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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