# Properties

 Label 4.4.16317.1-16.1-h Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $10$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.16317.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $10$ CM: no Base change: yes Newspace dimension: $30$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{10} - 45x^{8} + 738x^{6} - 5458x^{4} + 18300x^{2} - 22500$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-\frac{1}{150}e^{8} + \frac{3}{10}e^{6} - \frac{344}{75}e^{4} + \frac{2029}{75}e^{2} - 50$
7 $[7, 7, -w^{2} + 2]$ $-\frac{1}{150}e^{8} + \frac{3}{10}e^{6} - \frac{344}{75}e^{4} + \frac{2029}{75}e^{2} - 50$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{1}{75}e^{9} - \frac{49}{90}e^{7} + \frac{3403}{450}e^{5} - \frac{9274}{225}e^{3} + \frac{224}{3}e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{75}e^{9} - \frac{49}{90}e^{7} + \frac{3403}{450}e^{5} - \frac{9274}{225}e^{3} + \frac{224}{3}e$
25 $[25, 5, w^{2} - w - 3]$ $-\frac{11}{450}e^{8} + \frac{89}{90}e^{6} - \frac{3109}{225}e^{4} + \frac{5848}{75}e^{2} - 144$
37 $[37, 37, 2w - 1]$ $\phantom{-}\frac{4}{225}e^{8} - \frac{31}{45}e^{6} + \frac{1927}{225}e^{4} - \frac{2794}{75}e^{2} + 46$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-\frac{4}{225}e^{8} + \frac{31}{45}e^{6} - \frac{2002}{225}e^{4} + \frac{3269}{75}e^{2} - 66$
59 $[59, 59, 2w - 5]$ $-\frac{1}{225}e^{9} + \frac{13}{90}e^{7} - \frac{601}{450}e^{5} + \frac{533}{225}e^{3} + \frac{17}{3}e$
59 $[59, 59, -2w - 3]$ $-\frac{1}{225}e^{9} + \frac{13}{90}e^{7} - \frac{601}{450}e^{5} + \frac{533}{225}e^{3} + \frac{17}{3}e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}\frac{1}{50}e^{8} - \frac{9}{10}e^{6} + \frac{344}{25}e^{4} - \frac{2029}{25}e^{2} + 152$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{1}{50}e^{8} - \frac{9}{10}e^{6} + \frac{344}{25}e^{4} - \frac{2029}{25}e^{2} + 152$
83 $[83, 83, -w^{3} + 7w]$ $\phantom{-}\frac{1}{30}e^{9} - \frac{4}{3}e^{7} + \frac{181}{10}e^{5} - \frac{483}{5}e^{3} + 171e$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{7}{450}e^{9} - \frac{29}{45}e^{7} + \frac{4141}{450}e^{5} - \frac{3901}{75}e^{3} + 93e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{7}{450}e^{9} - \frac{29}{45}e^{7} + \frac{4141}{450}e^{5} - \frac{3901}{75}e^{3} + 93e$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{30}e^{9} - \frac{4}{3}e^{7} + \frac{181}{10}e^{5} - \frac{483}{5}e^{3} + 171e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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