# Properties

 Base field 4.4.18688.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.18688.1-16.1-l Dimension 4 CM yes Base change yes

# 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 $[16, 2, 2]$ Label 4.4.18688.1-16.1-l Dimension 4 Is CM yes Is base change yes Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut x^{3}$$ $$\mathstrut -\mathstrut 35x^{2}$$ $$\mathstrut -\mathstrut 45x$$ $$\mathstrut +\mathstrut 54$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $\phantom{-}0$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}e$
9 $[9, 3, w + 1]$ $\phantom{-}e$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} - \frac{35}{12}e - \frac{11}{2}$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}\frac{1}{12}e^{3} + \frac{1}{3}e^{2} - \frac{35}{12}e - \frac{11}{2}$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}0$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $\phantom{-}0$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{35}{6}e - 1$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{1}{3}e^{2} - \frac{35}{6}e - 1$
41 $[41, 41, 2w + 3]$ $\phantom{-}\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{23}{12}e + \frac{25}{2}$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $\phantom{-}\frac{1}{12}e^{3} - \frac{2}{3}e^{2} - \frac{23}{12}e + \frac{25}{2}$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $\phantom{-}0$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{39}{4}e - \frac{13}{2}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{1}{12}e^{3} - \frac{1}{3}e^{2} + \frac{59}{12}e + \frac{27}{2}$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-\frac{1}{12}e^{3} - \frac{1}{3}e^{2} + \frac{59}{12}e + \frac{27}{2}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $-\frac{1}{2}e^{3} + \frac{27}{2}e + 7$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $1$