# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 16 Level $[16, 2, 2]$ Label 4.4.8789.1-16.1-b Dimension 8 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

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

## Form

 Weight [2, 2, 2, 2] Level $[16, 2, 2]$ Label 4.4.8789.1-16.1-b Dimension 8 Is CM no Is base change no Parent newspace dimension 11

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8} - 30x^{6} + 2x^{5} + 229x^{4} - 35x^{3} - 334x^{2} + 184x - 8$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-\frac{641}{58998}e^{7} - \frac{127}{29499}e^{6} + \frac{10301}{29499}e^{5} + \frac{518}{9833}e^{4} - \frac{185411}{58998}e^{3} + \frac{26555}{58998}e^{2} + \frac{216038}{29499}e - \frac{78476}{29499}$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $-\frac{3877}{117996}e^{7} - \frac{223}{29499}e^{6} + \frac{59635}{58998}e^{5} + \frac{4529}{19666}e^{4} - \frac{958429}{117996}e^{3} - \frac{227981}{117996}e^{2} + \frac{796081}{58998}e - \frac{13529}{29499}$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{641}{58998}e^{7} - \frac{127}{29499}e^{6} + \frac{10301}{29499}e^{5} + \frac{518}{9833}e^{4} - \frac{185411}{58998}e^{3} + \frac{26555}{58998}e^{2} + \frac{245537}{29499}e - \frac{78476}{29499}$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $-\frac{2413}{29499}e^{7} - \frac{3431}{58998}e^{6} + \frac{71204}{29499}e^{5} + \frac{15359}{9833}e^{4} - \frac{521341}{29499}e^{3} - \frac{548683}{58998}e^{2} + \frac{1235281}{58998}e - \frac{107714}{29499}$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $\phantom{-}\frac{2819}{39332}e^{7} + \frac{129}{19666}e^{6} - \frac{41743}{19666}e^{5} - \frac{2585}{19666}e^{4} + \frac{617731}{39332}e^{3} + \frac{27689}{39332}e^{2} - \frac{193649}{9833}e + \frac{51160}{9833}$
17 $[17, 17, -w^{2} + 2w + 1]$ $-\frac{10847}{117996}e^{7} - \frac{6475}{58998}e^{6} + \frac{159587}{58998}e^{5} + \frac{58851}{19666}e^{4} - \frac{2317535}{117996}e^{3} - \frac{2229661}{117996}e^{2} + \frac{624835}{29499}e + \frac{115046}{29499}$
19 $[19, 19, w^{2} - w - 2]$ $\phantom{-}\frac{1395}{19666}e^{7} + \frac{1059}{19666}e^{6} - \frac{20301}{9833}e^{5} - \frac{14841}{9833}e^{4} + \frac{285757}{19666}e^{3} + \frac{105706}{9833}e^{2} - \frac{267735}{19666}e - \frac{49252}{9833}$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-\frac{9011}{58998}e^{7} - \frac{3304}{29499}e^{6} + \frac{132107}{29499}e^{5} + \frac{30200}{9833}e^{4} - \frac{1899953}{58998}e^{3} - \frac{1182919}{58998}e^{2} + \frac{1019243}{29499}e - \frac{18956}{29499}$
29 $[29, 29, w^{2} - w - 3]$ $-\frac{1195}{58998}e^{7} - \frac{3044}{29499}e^{6} + \frac{17179}{29499}e^{5} + \frac{28133}{9833}e^{4} - \frac{232171}{58998}e^{3} - \frac{1073297}{58998}e^{2} + \frac{14389}{29499}e + \frac{268526}{29499}$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{17155}{58998}e^{7} + \frac{5930}{29499}e^{6} - \frac{254515}{29499}e^{5} - \frac{52060}{9833}e^{4} + \frac{3764959}{58998}e^{3} + \frac{1883015}{58998}e^{2} - \frac{2271370}{29499}e + \frac{391510}{29499}$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $-\frac{2204}{9833}e^{7} - \frac{2437}{19666}e^{6} + \frac{65269}{9833}e^{5} + \frac{30782}{9833}e^{4} - \frac{483928}{9833}e^{3} - \frac{343599}{19666}e^{2} + \frac{1233509}{19666}e - \frac{101946}{9833}$
47 $[47, 47, w^{3} - 7w - 4]$ $-\frac{127}{29499}e^{7} + \frac{686}{29499}e^{6} + \frac{2195}{29499}e^{5} - \frac{6437}{9833}e^{4} + \frac{2060}{29499}e^{3} + \frac{108991}{29499}e^{2} - \frac{19504}{29499}e - \frac{2564}{29499}$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-\frac{4873}{19666}e^{7} - \frac{1395}{9833}e^{6} + \frac{72036}{9833}e^{5} + \frac{35729}{9833}e^{4} - \frac{1056553}{19666}e^{3} - \frac{420625}{19666}e^{2} + \frac{622045}{9833}e - \frac{52752}{9833}$
61 $[61, 61, -w - 3]$ $-\frac{288}{9833}e^{7} + \frac{162}{9833}e^{6} + \frac{9778}{9833}e^{5} - \frac{4847}{9833}e^{4} - \frac{92110}{9833}e^{3} + \frac{33622}{9833}e^{2} + \frac{208796}{9833}e - \frac{35236}{9833}$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $\phantom{-}\frac{15355}{39332}e^{7} + \frac{1989}{9833}e^{6} - \frac{226417}{19666}e^{5} - \frac{103725}{19666}e^{4} + \frac{3302351}{39332}e^{3} + \frac{1252431}{39332}e^{2} - \frac{1918789}{19666}e + \frac{182489}{9833}$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}\frac{24745}{117996}e^{7} + \frac{5639}{58998}e^{6} - \frac{370045}{58998}e^{5} - \frac{46305}{19666}e^{4} + \frac{5583205}{117996}e^{3} + \frac{1483259}{117996}e^{2} - \frac{1862573}{29499}e + \frac{526034}{29499}$
81 $[81, 3, -3]$ $\phantom{-}\frac{2678}{9833}e^{7} + \frac{2181}{9833}e^{6} - \frac{78494}{9833}e^{5} - \frac{57425}{9833}e^{4} + \frac{566285}{9833}e^{3} + \frac{343032}{9833}e^{2} - \frac{620340}{9833}e + \frac{82094}{9833}$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}\frac{39593}{117996}e^{7} + \frac{5648}{29499}e^{6} - \frac{580583}{58998}e^{5} - \frac{95703}{19666}e^{4} + \frac{8361017}{117996}e^{3} + \frac{3248221}{117996}e^{2} - \frac{4596281}{58998}e + \frac{421891}{29499}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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