# Properties

 Base field 4.4.13068.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9, 3, -w^{2} + 2w + 2]$ Label 4.4.13068.1-9.1-c 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 $[9, 3, -w^{2} + 2w + 2]$ Label 4.4.13068.1-9.1-c Dimension 6 Is CM no Is base change yes Parent newspace dimension 10

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 14x^{4}$$ $$\mathstrut +\mathstrut 59x^{2}$$ $$\mathstrut -\mathstrut 72$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}0$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}e^{4} - 9e^{2} + 17$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{9}{2}e$
17 $[17, 17, -w + 2]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{9}{2}e$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{13}{2}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $-\frac{1}{2}e^{5} + 4e^{3} - \frac{13}{2}e$
31 $[31, 31, -w^{2} + 2]$ $-2e^{2} + 8$
31 $[31, 31, -w^{3} + 7w + 5]$ $-2e^{2} + 8$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $-2e^{2} + 8$
67 $[67, 67, -w^{2} + 4w + 2]$ $-2e^{2} + 8$
83 $[83, 83, 2w^{2} - 5w - 2]$ $\phantom{-}e^{5} - 10e^{3} + 19e$
83 $[83, 83, -w^{3} + 8w + 6]$ $-2e^{5} + 20e^{3} - 44e$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $\phantom{-}e^{5} - 10e^{3} + 19e$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $-2e^{5} + 20e^{3} - 44e$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $-2e^{4} + 20e^{2} - 34$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $-2e^{4} + 20e^{2} - 34$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $\phantom{-}2e^{4} - 22e^{2} + 56$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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