# Properties

 Label 4.4.8069.1-16.1-e Base field 4.4.8069.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8069.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} - 22x^{2} + 100$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $-\frac{1}{10}e^{3} + \frac{6}{5}e$
7 $[7, 7, w + 1]$ $\phantom{-}e$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + 3]$ $-\frac{1}{10}e^{3} + \frac{11}{5}e$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $-\frac{3}{10}e^{3} + \frac{18}{5}e$
17 $[17, 17, -w^{3} + 5w - 2]$ $\phantom{-}e^{2} - 12$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}e^{2} - 10$
19 $[19, 19, -w^{2} - w + 1]$ $-\frac{1}{5}e^{3} + \frac{17}{5}e$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $-\frac{1}{2}e^{3} + 6e$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{3}{10}e^{3} - \frac{23}{5}e$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{24}{5}e$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}10$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $-e^{2} + 10$
49 $[49, 7, w^{2} + 2w - 2]$ $\phantom{-}e^{2} - 14$
59 $[59, 59, 2w^{3} - 8w + 3]$ $-e$
67 $[67, 67, w^{2} - w - 4]$ $\phantom{-}0$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-\frac{1}{5}e^{3} + \frac{12}{5}e$
81 $[81, 3, -3]$ $-e^{2} + 10$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$