# Properties

 Base field $$\Q(\sqrt{2}, \sqrt{3})$$ Weight [2, 2, 2, 2] Level norm 47 Level $[47,47,3w^{3} + 2w^{2} - 12w - 8]$ Label 4.4.2304.1-47.4-a Dimension 1 CM no Base change no

# Related objects

## Base field $$\Q(\sqrt{2}, \sqrt{3})$$

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

## Form

 Weight [2, 2, 2, 2] Level $[47,47,3w^{3} + 2w^{2} - 12w - 8]$ Label 4.4.2304.1-47.4-a Dimension 1 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w + 1]$ $\phantom{-}2$
9 $[9, 3, -w^{2} + 2]$ $-2$
23 $[23, 23, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}0$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}4$
23 $[23, 23, -w^{2} - w + 3]$ $\phantom{-}4$
23 $[23, 23, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}8$
25 $[25, 5, w^{3} - 5w + 1]$ $\phantom{-}2$
25 $[25, 5, w^{3} - 5w - 1]$ $-2$
47 $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ $\phantom{-}8$
47 $[47, 47, -2w^{3} - w^{2} + 6w]$ $-4$
47 $[47, 47, 2w^{3} - w^{2} - 6w]$ $\phantom{-}0$
47 $[47, 47, w^{2} + w - 5]$ $-1$
49 $[49, 7, 2w^{3} - 6w - 1]$ $-6$
49 $[49, 7, -2w^{3} + 6w - 1]$ $\phantom{-}2$
71 $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ $\phantom{-}8$
71 $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ $\phantom{-}0$
71 $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ $\phantom{-}8$
71 $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ $\phantom{-}0$
73 $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ $-2$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
47 $[47,47,3w^{3} + 2w^{2} - 12w - 8]$ $1$