# Properties

 Base field 4.4.18432.1 Weight [2, 2, 2, 2] Level norm 8 Level $[8, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 2]$ Label 4.4.18432.1-8.1-b Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18432.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 18$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[8, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 2w - 2]$ Label 4.4.18432.1-8.1-b Dimension 4 Is CM no Is base change no Parent newspace dimension 8

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 12x^{2}$$ $$\mathstrut -\mathstrut 16x$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{2}e^{3} + 6e + 6$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{2}e^{3} + e^{2} + 4e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e^{3} - e^{2} - 11e - 6$
9 $[9, 3, w - 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-e^{3} - e^{2} + 14e + 14$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $-e^{3} + e^{2} + 14e + 2$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}3e^{3} - 3e^{2} - 34e - 22$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-e^{3} + 3e^{2} + 6e - 10$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $-e^{3} + 2e^{2} + 6e - 4$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}e^{3} - 10e - 16$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}3e^{3} - 4e^{2} - 30e - 16$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $-3e^{3} + 2e^{2} + 34e + 20$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}2e^{3} - 4e^{2} - 16e$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-4e$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-4e^{3} + 4e^{2} + 44e + 24$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}2e^{3} - 24e - 24$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $-2e^{3} + 3e^{2} + 22e + 2$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $\phantom{-}e^{3} + e^{2} - 16e - 22$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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