# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-e Dimension 16 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1129.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 3$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-e Dimension 16 Is CM no Is base change no Parent newspace dimension 36

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{16}$$ $$\mathstrut -\mathstrut 38x^{14}$$ $$\mathstrut +\mathstrut 570x^{12}$$ $$\mathstrut -\mathstrut 4330x^{10}$$ $$\mathstrut +\mathstrut 17802x^{8}$$ $$\mathstrut -\mathstrut 39556x^{6}$$ $$\mathstrut +\mathstrut 46044x^{4}$$ $$\mathstrut -\mathstrut 26272x^{2}$$ $$\mathstrut +\mathstrut 5776$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $-\frac{2383}{83596}e^{14} + \frac{88451}{83596}e^{12} - \frac{638999}{41798}e^{10} + \frac{2279976}{20899}e^{8} - \frac{8393043}{20899}e^{6} + \frac{30300539}{41798}e^{4} - \frac{11818090}{20899}e^{2} + \frac{3177061}{20899}$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1469529}{12706592}e^{15} - \frac{717255}{167192}e^{13} + \frac{20739811}{334384}e^{11} - \frac{2822284403}{6353296}e^{9} + \frac{10497720375}{6353296}e^{7} - \frac{4856516049}{1588324}e^{5} + \frac{7978362867}{3176648}e^{3} - \frac{1153443205}{1588324}e$
8 $[8, 2, 2]$ $-\frac{2383}{83596}e^{14} + \frac{88451}{83596}e^{12} - \frac{638999}{41798}e^{10} + \frac{2279976}{20899}e^{8} - \frac{8393043}{20899}e^{6} + \frac{30300539}{41798}e^{4} - \frac{11818090}{20899}e^{2} + \frac{3156162}{20899}$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}\frac{56599}{12706592}e^{15} - \frac{29191}{167192}e^{13} + \frac{908053}{334384}e^{11} - \frac{136320613}{6353296}e^{9} + \frac{580760993}{6353296}e^{7} - \frac{326035241}{1588324}e^{5} + \frac{697044285}{3176648}e^{3} - \frac{131840835}{1588324}e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}\frac{2077463}{12706592}e^{15} - \frac{1012613}{167192}e^{13} + \frac{29228309}{334384}e^{11} - \frac{3967938869}{6353296}e^{9} + \frac{14709940665}{6353296}e^{7} - \frac{6771366171}{1588324}e^{5} + \frac{11040937269}{3176648}e^{3} - \frac{1580258035}{1588324}e$
17 $[17, 17, -w^{2} + w + 4]$ $-\frac{255633}{3176648}e^{15} + \frac{62364}{20899}e^{13} - \frac{3605457}{83596}e^{11} + \frac{490586225}{1588324}e^{9} - \frac{1825942167}{1588324}e^{7} + \frac{847142287}{397081}e^{5} - \frac{1404114533}{794162}e^{3} + \frac{206647228}{397081}e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}1$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}\frac{2362103}{12706592}e^{15} - \frac{1149607}{167192}e^{13} + \frac{33111549}{334384}e^{11} - \frac{4481013709}{6353296}e^{9} + \frac{16529895441}{6353296}e^{7} - \frac{7542582645}{1588324}e^{5} + \frac{12088041725}{3176648}e^{3} - \frac{1681021739}{1588324}e$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}\frac{689689}{6353296}e^{15} - \frac{336335}{83596}e^{13} + \frac{9714711}{167192}e^{11} - \frac{1320222079}{3176648}e^{9} + \frac{4903248391}{3176648}e^{7} - \frac{2265670901}{794162}e^{5} + \frac{3729105827}{1588324}e^{3} - \frac{546340169}{794162}e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}\frac{35345}{3176648}e^{15} - \frac{8829}{20899}e^{13} + \frac{528511}{83596}e^{11} - \frac{75786853}{1588324}e^{9} + \frac{305806907}{1588324}e^{7} - \frac{160640415}{397081}e^{5} + \frac{315649835}{794162}e^{3} - \frac{54309623}{397081}e$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}\frac{307687}{12706592}e^{15} - \frac{150791}{167192}e^{13} + \frac{4388957}{334384}e^{11} - \frac{603875821}{6353296}e^{9} + \frac{2290253169}{6353296}e^{7} - \frac{1098112709}{1588324}e^{5} + \frac{1917865165}{3176648}e^{3} - \frac{290975915}{1588324}e$
59 $[59, 59, 2w^{2} - 13]$ $-\frac{11533}{83596}e^{14} + \frac{213411}{41798}e^{12} - \frac{3075671}{41798}e^{10} + \frac{21928215}{41798}e^{8} - \frac{80984315}{41798}e^{6} + \frac{73984492}{20899}e^{4} - \frac{59278825}{20899}e^{2} + \frac{16394892}{20899}$
61 $[61, 61, w^{2} + w - 10]$ $-\frac{127283}{334384}e^{14} + \frac{1179425}{83596}e^{12} - \frac{34059207}{167192}e^{10} + \frac{243387753}{167192}e^{8} - \frac{901513477}{167192}e^{6} + \frac{413535145}{41798}e^{4} - \frac{667435953}{83596}e^{2} + \frac{93835003}{41798}$
67 $[67, 67, 2w^{2} - w - 11]$ $-\frac{3427159}{6353296}e^{15} + \frac{417776}{20899}e^{13} - \frac{48259645}{167192}e^{11} + \frac{6556211577}{3176648}e^{9} - \frac{24328731965}{3176648}e^{7} + \frac{5605936520}{397081}e^{5} - \frac{18286799729}{1588324}e^{3} + \frac{2615630243}{794162}e$
73 $[73, 73, -w^{2} - 1]$ $-\frac{6767}{83596}e^{14} + \frac{62480}{20899}e^{12} - \frac{1797673}{41798}e^{10} + \frac{12808311}{41798}e^{8} - \frac{47412143}{41798}e^{6} + \frac{43683953}{20899}e^{4} - \frac{35684443}{20899}e^{2} + \frac{10416952}{20899}$
83 $[83, 83, w^{2} - w - 10]$ $-\frac{132927}{334384}e^{14} + \frac{1231561}{83596}e^{12} - \frac{35563975}{167192}e^{10} + \frac{254218365}{167192}e^{8} - \frac{942734297}{167192}e^{6} + \frac{433906537}{41798}e^{4} - \frac{706290329}{83596}e^{2} + \frac{100889251}{41798}$
89 $[89, 89, -w^{2} + 4w - 2]$ $-\frac{9841}{41798}e^{14} + \frac{363607}{41798}e^{12} - \frac{2615096}{20899}e^{10} + \frac{18606314}{20899}e^{8} - \frac{68607519}{20899}e^{6} + \frac{125453971}{20899}e^{4} - \frac{101405260}{20899}e^{2} + \frac{28870464}{20899}$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}\frac{302079}{1588324}e^{15} - \frac{587859}{83596}e^{13} + \frac{4229323}{41798}e^{11} - \frac{285640662}{397081}e^{9} + \frac{1049445459}{397081}e^{7} - \frac{3797945209}{794162}e^{5} + \frac{1495815780}{397081}e^{3} - \frac{406684372}{397081}e$
97 $[97, 97, -w^{2} - 4w - 5]$ $\phantom{-}\frac{104013}{334384}e^{14} - \frac{962367}{83596}e^{12} + \frac{27748729}{167192}e^{10} - \frac{198058143}{167192}e^{8} + \frac{733647515}{167192}e^{6} - \frac{337718525}{41798}e^{4} + \frac{551954875}{83596}e^{2} - \frac{79566617}{41798}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} - w + 4]$ $-1$