# Properties

 Base field 4.4.13068.1 Weight [2, 2, 2, 2] Level norm 4 Level $[4, 2, w^{3} - w^{2} - 5w - 2]$ Label 4.4.13068.1-4.2-a Dimension 6 CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.13068.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} - x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[4, 2, w^{3} - w^{2} - 5w - 2]$ Label 4.4.13068.1-4.2-a Dimension 6 Is CM no Is base change yes Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 13x^{4}$$ $$\mathstrut +\mathstrut 43x^{2}$$ $$\mathstrut -\mathstrut 23$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{1}{4}e^{4} + \frac{5}{2}e^{2} - \frac{13}{4}$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $-1$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{41}{4}e$
17 $[17, 17, -w + 2]$ $-\frac{1}{4}e^{5} + \frac{7}{2}e^{3} - \frac{41}{4}e$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $\phantom{-}e^{3} - 9e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}e^{3} - 9e$
31 $[31, 31, -w^{2} + 2]$ $-e^{4} + 8e^{2} - 9$
31 $[31, 31, -w^{3} + 7w + 5]$ $-e^{4} + 8e^{2} - 9$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $-\frac{1}{2}e^{5} + 5e^{3} - \frac{21}{2}e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $-\frac{1}{2}e^{4} + 2e^{2} + \frac{21}{2}$
67 $[67, 67, -w^{2} + 4w + 2]$ $-\frac{1}{2}e^{4} + 2e^{2} + \frac{21}{2}$
83 $[83, 83, 2w^{2} - 5w - 2]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{25}{2}e$
83 $[83, 83, -w^{3} + 8w + 6]$ $-e^{5} + 9e^{3} - 12e$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{25}{2}e$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $-e^{5} + 9e^{3} - 12e$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{2} - \frac{11}{4}$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{4}e^{4} - \frac{1}{2}e^{2} - \frac{11}{4}$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $\phantom{-}\frac{5}{4}e^{4} - \frac{21}{2}e^{2} + \frac{25}{4}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $1$