# Properties

 Base field $$\Q(\sqrt{2}, \sqrt{3})$$ Weight [2, 2, 2, 2] Level norm 71 Level $[71,71,-w^{3} + w^{2} + 2w - 3]$ Label 4.4.2304.1-71.2-a Dimension 3 CM no Base change no

# Related objects

• L-function not available

## 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 $[71,71,-w^{3} + w^{2} + 2w - 3]$ Label 4.4.2304.1-71.2-a Dimension 3 Is CM no Is base change no Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} - 3x^{2} + 3$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w + 1]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e - 2$
23 $[23, 23, w^{3} - w^{2} - 4w + 1]$ $-2e^{2} + 2e + 9$
23 $[23, 23, w^{2} - w - 3]$ $-e + 3$
23 $[23, 23, -w^{2} - w + 3]$ $-4e^{2} + 5e + 9$
23 $[23, 23, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}5e^{2} - 7e - 6$
25 $[25, 5, w^{3} - 5w + 1]$ $-5e^{2} + 6e + 8$
25 $[25, 5, w^{3} - 5w - 1]$ $\phantom{-}4e^{2} - 9e - 4$
47 $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ $-3e^{2} + 7e + 9$
47 $[47, 47, -2w^{3} - w^{2} + 6w]$ $\phantom{-}e^{2} - 5e + 6$
47 $[47, 47, 2w^{3} - w^{2} - 6w]$ $\phantom{-}e^{2} - 2e$
47 $[47, 47, w^{2} + w - 5]$ $\phantom{-}2e^{2} - 2e - 3$
49 $[49, 7, 2w^{3} - 6w - 1]$ $\phantom{-}e^{2} - 7$
49 $[49, 7, -2w^{3} + 6w - 1]$ $\phantom{-}e^{2} - 3e - 10$
71 $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ $\phantom{-}3e^{2} - 6e$
71 $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ $-1$
71 $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ $-5e^{2} + 12e + 3$
71 $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ $-5e^{2} + 3e + 15$
73 $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ $-6e^{2} + 15e + 2$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
71 $[71,71,-w^{3} + w^{2} + 2w - 3]$ $1$