# Properties

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

# 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: no Newspace dimension: $30$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{10} - 33x^{8} + 368x^{6} - 1722x^{4} + 3500x^{2} - 2500$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $-e$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}\frac{61}{50}e^{8} - \frac{1813}{50}e^{6} + \frac{8249}{25}e^{4} - \frac{25421}{25}e^{2} + 926$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}\frac{61}{50}e^{8} - \frac{1813}{50}e^{6} + \frac{8249}{25}e^{4} - \frac{25421}{25}e^{2} + 926$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $\phantom{-}\frac{8}{25}e^{8} - \frac{239}{25}e^{6} + \frac{2194}{25}e^{4} - \frac{6851}{25}e^{2} + 250$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{42}{25}e^{9} - \frac{2497}{50}e^{7} + \frac{22737}{50}e^{5} - \frac{35099}{25}e^{3} + 1282e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $-\frac{42}{25}e^{9} + \frac{2497}{50}e^{7} - \frac{22737}{50}e^{5} + \frac{35099}{25}e^{3} - 1282e$
25 $[25, 5, w^{2} - w - 3]$ $\phantom{-}\frac{107}{50}e^{8} - \frac{3181}{50}e^{6} + \frac{14488}{25}e^{4} - \frac{44802}{25}e^{2} + 1638$
37 $[37, 37, 2w - 1]$ $-\frac{23}{25}e^{8} + \frac{684}{25}e^{6} - \frac{6239}{25}e^{4} + \frac{19356}{25}e^{2} - 710$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}\frac{53}{25}e^{8} - \frac{1574}{25}e^{6} + \frac{14304}{25}e^{4} - \frac{43991}{25}e^{2} + 1600$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $\phantom{-}\frac{53}{25}e^{8} - \frac{1574}{25}e^{6} + \frac{14304}{25}e^{4} - \frac{43991}{25}e^{2} + 1600$
59 $[59, 59, 2w - 5]$ $\phantom{-}\frac{34}{25}e^{9} - \frac{2019}{50}e^{7} + \frac{18349}{50}e^{5} - \frac{28248}{25}e^{3} + 1031e$
59 $[59, 59, -2w - 3]$ $-\frac{34}{25}e^{9} + \frac{2019}{50}e^{7} - \frac{18349}{50}e^{5} + \frac{28248}{25}e^{3} - 1031e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}\frac{307}{50}e^{8} - \frac{9131}{50}e^{6} + \frac{41613}{25}e^{4} - \frac{128727}{25}e^{2} + 4724$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}\frac{307}{50}e^{8} - \frac{9131}{50}e^{6} + \frac{41613}{25}e^{4} - \frac{128727}{25}e^{2} + 4724$
83 $[83, 83, -w^{3} + 7w]$ $-\frac{67}{50}e^{9} + \frac{993}{25}e^{7} - \frac{17981}{50}e^{5} + \frac{27412}{25}e^{3} - 981e$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{39}{50}e^{9} - \frac{581}{25}e^{7} + \frac{10627}{50}e^{5} - \frac{16554}{25}e^{3} + 613e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $-\frac{39}{50}e^{9} + \frac{581}{25}e^{7} - \frac{10627}{50}e^{5} + \frac{16554}{25}e^{3} - 613e$
83 $[83, 83, w^{2} - 2w - 6]$ $\phantom{-}\frac{67}{50}e^{9} - \frac{993}{25}e^{7} + \frac{17981}{50}e^{5} - \frac{27412}{25}e^{3} + 981e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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