# Properties

 Base field 4.4.18432.1 Weight [2, 2, 2, 2] Level norm 14 Level $[14,14,-\frac{1}{3}w^{3} + 3w + 2]$ Label 4.4.18432.1-14.2-d Dimension 2 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 $[14,14,-\frac{1}{3}w^{3} + 3w + 2]$ Label 4.4.18432.1-14.2-d Dimension 2 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2}$$ $$\mathstrut +\mathstrut 2x$$ $$\mathstrut -\mathstrut 7$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}1$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-\frac{1}{2}e - \frac{1}{2}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{2}e - \frac{5}{2}$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $-1$
9 $[9, 3, w - 3]$ $\phantom{-}\frac{1}{2}e + \frac{1}{2}$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-2e - 6$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}\frac{5}{2}e + \frac{13}{2}$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-e + 3$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{3}{2}e - \frac{5}{2}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}\frac{3}{2}e + \frac{1}{2}$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-\frac{1}{2}e - \frac{17}{2}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}e + 4$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $-3e + 1$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-\frac{3}{2}e - \frac{29}{2}$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}3e - 6$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}\frac{3}{2}e + \frac{7}{2}$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-3e + 3$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}\frac{3}{2}e - \frac{17}{2}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-\frac{3}{2}e - \frac{15}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,\frac{1}{3}w^{2} - w]$ $-1$
7 $[7,7,-\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - 3]$ $1$