# Properties

 Base field 4.4.18688.1 Weight [2, 2, 2, 2] Level norm 9 Level $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ Label 4.4.18688.1-9.1-a Dimension 3 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18688.1

Generator $$w$$, with minimal polynomial $$x^{4} - 10x^{2} - 4x + 14$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ Label 4.4.18688.1-9.1-a Dimension 3 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3}$$ $$\mathstrut -\mathstrut x^{2}$$ $$\mathstrut -\mathstrut 10x$$ $$\mathstrut -\mathstrut 4$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 3$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}1$
9 $[9, 3, w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
17 $[17, 17, w + 3]$ $-e^{2} + 2e + 6$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 4$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $-e^{2} + e + 6$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 4$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $-2e - 2$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 6$
41 $[41, 41, 2w + 3]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $\phantom{-}2e^{2} - 4e - 14$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 4$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 3$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $-e^{2} + 3e + 2$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{3}{2}e^{2} - \frac{1}{2}e + 9$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-\frac{3}{2}e^{2} + \frac{9}{2}e + 8$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-e^{2} + e$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $-e^{2} + e - 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $-1$