# Properties

 Base field 4.4.2624.1 Weight [2, 2, 2, 2] Level norm 68 Level $[68, 34, -w^{3} + w^{2} + 5w - 2]$ Label 4.4.2624.1-68.1-c Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.2624.1

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

## Form

 Weight [2, 2, 2, 2] Level $[68, 34, -w^{3} + w^{2} + 5w - 2]$ Label 4.4.2624.1-68.1-c Dimension 2 Is CM no Is base change no Parent newspace dimension 5

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 20$$
Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $-1$
7 $[7, 7, -w^{3} + 3w^{2} + w - 3]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + w + 2]$ $-\frac{1}{2}e - 1$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $-1$
17 $[17, 17, -w^{3} + w^{2} + 4w]$ $\phantom{-}4$
25 $[25, 5, -w^{3} + 3w^{2} + 2w - 2]$ $\phantom{-}e + 4$
25 $[25, 5, -2w^{3} + 4w^{2} + 5w - 1]$ $\phantom{-}e + 4$
41 $[41, 41, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{1}{2}e - 1$
47 $[47, 47, -2w^{3} + 5w^{2} + 4w - 4]$ $\phantom{-}\frac{1}{2}e - 9$
47 $[47, 47, 2w^{3} - 4w^{2} - 5w]$ $-2$
49 $[49, 7, w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{2}e + 3$
71 $[71, 71, 2w - 3]$ $-e + 10$
71 $[71, 71, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}3e - 2$
73 $[73, 73, -w^{3} + 3w^{2} + 3w - 5]$ $-e - 4$
73 $[73, 73, 2w^{3} - 5w^{2} - 5w + 4]$ $\phantom{-}4$
73 $[73, 73, -w^{3} + 3w^{2} - 5]$ $-e + 8$
73 $[73, 73, w^{3} - w^{2} - 4w + 2]$ $-\frac{1}{2}e + 1$
79 $[79, 79, 2w^{3} - 3w^{2} - 6w + 2]$ $-e + 2$
79 $[79, 79, 2w^{3} - 3w^{2} - 5w]$ $-2e - 6$
81 $[81, 3, -3]$ $-e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - 2w^{2} - 2w + 1]$ $1$
17 $[17, 17, -w^{3} + 3w^{2} - 3]$ $1$