# Properties

 Base field 4.4.13068.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$ Label 4.4.13068.1-16.3-d Dimension 8 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.13068.1

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

## Form

 Weight [2, 2, 2, 2] Level $[16, 4, 3w^{3} - 5w^{2} - 15w + 6]$ Label 4.4.13068.1-16.3-d Dimension 8 Is CM no Is base change no Parent newspace dimension 25

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8}$$ $$\mathstrut -\mathstrut 112x^{6}$$ $$\mathstrut +\mathstrut 3824x^{4}$$ $$\mathstrut -\mathstrut 41600x^{2}$$ $$\mathstrut +\mathstrut 40000$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - w^{2} - 6w - 2]$ $-\frac{1}{112000}e^{7} - \frac{11}{14000}e^{5} + \frac{1697}{14000}e^{3} - \frac{167}{70}e$
3 $[3, 3, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2800}e^{6} - \frac{87}{2800}e^{4} + \frac{114}{175}e^{2} - \frac{15}{14}$
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $\phantom{-}0$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{56000}e^{7} - \frac{11}{7000}e^{5} + \frac{1697}{7000}e^{3} - \frac{202}{35}e$
17 $[17, 17, -w + 2]$ $\phantom{-}e$
29 $[29, 29, -w^{3} + 2w^{2} + 4w - 4]$ $-\frac{41}{112000}e^{7} + \frac{1023}{28000}e^{5} - \frac{13723}{14000}e^{3} + \frac{957}{140}e$
29 $[29, 29, w^{3} - 2w^{2} - 4w]$ $\phantom{-}\frac{1}{16000}e^{7} - \frac{7}{1000}e^{5} + \frac{603}{2000}e^{3} - \frac{28}{5}e$
31 $[31, 31, -w^{2} + 2]$ $-\frac{1}{11200}e^{6} - \frac{11}{1400}e^{4} + \frac{997}{1400}e^{2} - \frac{34}{7}$
31 $[31, 31, -w^{3} + 7w + 5]$ $-\frac{1}{1600}e^{6} + \frac{7}{100}e^{4} - \frac{403}{200}e^{2} + 9$
41 $[41, 41, -2w^{3} + 2w^{2} + 13w - 2]$ $\phantom{-}\frac{27}{112000}e^{7} - \frac{403}{14000}e^{5} + \frac{15081}{14000}e^{3} - \frac{179}{14}e$
41 $[41, 41, 3w^{3} - 4w^{2} - 17w + 5]$ $-\frac{3}{16000}e^{7} + \frac{59}{4000}e^{5} - \frac{409}{2000}e^{3} - \frac{7}{20}e$
67 $[67, 67, 3w^{3} - 4w^{2} - 17w + 1]$ $\phantom{-}\frac{3}{1400}e^{6} - \frac{261}{1400}e^{4} + \frac{1193}{350}e^{2} + \frac{32}{7}$
67 $[67, 67, -w^{2} + 4w + 2]$ $-\frac{1}{1400}e^{6} + \frac{87}{1400}e^{4} - \frac{281}{350}e^{2} - \frac{48}{7}$
83 $[83, 83, 2w^{2} - 5w - 2]$ $-\frac{1}{4480}e^{7} + \frac{17}{560}e^{5} - \frac{739}{560}e^{3} + \frac{1299}{70}e$
83 $[83, 83, -w^{3} + 8w + 6]$ $-\frac{79}{112000}e^{7} + \frac{1937}{28000}e^{5} - \frac{26237}{14000}e^{3} + \frac{383}{28}e$
83 $[83, 83, w^{3} - 2w^{2} - 2w - 2]$ $\phantom{-}\frac{3}{16000}e^{7} - \frac{59}{4000}e^{5} + \frac{409}{2000}e^{3} - \frac{13}{20}e$
83 $[83, 83, w^{3} - 2w^{2} - 6w]$ $\phantom{-}\frac{69}{112000}e^{7} - \frac{51}{875}e^{5} + \frac{20807}{14000}e^{3} - \frac{353}{35}e$
97 $[97, 97, -3w^{3} + 2w^{2} + 17w + 7]$ $\phantom{-}\frac{33}{11200}e^{6} - \frac{337}{1400}e^{4} + \frac{5599}{1400}e^{2} + \frac{44}{7}$
97 $[97, 97, w^{3} - 4w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{1600}e^{6} - \frac{7}{100}e^{4} + \frac{503}{200}e^{2} - 19$
97 $[97, 97, -5w^{3} + 8w^{2} + 24w - 8]$ $-\frac{3}{1400}e^{6} + \frac{261}{1400}e^{4} - \frac{684}{175}e^{2} + \frac{136}{7}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{3} - w^{2} - 5w - 2]$ $1$