# Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.8768.1-16.1-a Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.8768.1-16.1-a Dimension 2 Is CM no Is base change no Parent newspace dimension 7

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 4x - 1$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-\frac{1}{2}e + \frac{5}{2}$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}\frac{1}{2}e - \frac{9}{2}$
7 $[7, 7, w - 1]$ $-3$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e + \frac{3}{2}$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{5}{2}e + \frac{5}{2}$
31 $[31, 31, w^{2} - 5]$ $-3e + 6$
31 $[31, 31, -w^{2} + 2w + 4]$ $-5$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}2e + 1$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-5$
47 $[47, 47, w^{2} - 2w - 5]$ $\phantom{-}\frac{3}{2}e - \frac{13}{2}$
47 $[47, 47, w^{2} - 6]$ $-\frac{1}{2}e - \frac{5}{2}$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $-1$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-e - 4$
79 $[79, 79, -w - 3]$ $\phantom{-}\frac{3}{2}e - \frac{23}{2}$
79 $[79, 79, w - 4]$ $-\frac{7}{2}e + \frac{7}{2}$
81 $[81, 3, -3]$ $\phantom{-}e - 10$
89 $[89, 89, w^{2} - 3w - 2]$ $-\frac{11}{2}e + \frac{15}{2}$
89 $[89, 89, w^{2} + w - 4]$ $-\frac{3}{2}e - \frac{1}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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