# Properties

 Base field 4.4.13888.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.13888.1-16.1-e Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13888.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 6x + 9$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.13888.1-16.1-e Dimension 4 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 24x^{2}$$ $$\mathstrut +\mathstrut 64$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $\phantom{-}\frac{1}{16}e^{3} - e$
7 $[7, 7, w - 2]$ $\phantom{-}0$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{1}{16}e^{3} - e$
9 $[9, 3, w]$ $\phantom{-}\frac{1}{16}e^{3} - 2e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $-\frac{1}{16}e^{3} + 2e$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - 10$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-\frac{1}{2}e^{2} + 2$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-4$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $-\frac{3}{8}e^{3} + 8e$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-\frac{1}{8}e^{3}$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $-\frac{5}{16}e^{3} + 7e$
47 $[47, 47, w^{2} - w - 4]$ $-\frac{1}{16}e^{3} - e$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $-\frac{3}{16}e^{3} + 2e$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-e^{2} + 10$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}e^{2} - 14$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $-\frac{5}{16}e^{3} + 6e$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}\frac{1}{16}e^{3} + e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}\frac{5}{16}e^{3} - 7e$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $\phantom{-}\frac{3}{16}e^{3} - 4e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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