Properties

Label 6.6.905177.1-41.1-c
Base field 6.6.905177.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $41$
Level $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$
Dimension $14$
CM no
Base change no

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Base field 6.6.905177.1

Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 9x^{3} + 7x^{2} - 9x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$
Dimension: $14$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

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

\(x^{14} - 80x^{12} + 2430x^{10} - 35104x^{8} + 243921x^{6} - 698672x^{4} + 403600x^{2} - 40000\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, -2w^{5} - w^{4} + 13w^{3} + w^{2} - 16w - 1]$ $\phantom{-}e$
8 $[8, 2, -3w^{5} - w^{4} + 19w^{3} - 2w^{2} - 20w + 1]$ $\phantom{-}\frac{9163433}{129394111000}e^{13} - \frac{41455763}{7393949200}e^{11} + \frac{8682340451}{51757644400}e^{9} - \frac{612665881689}{258788222000}e^{7} + \frac{4088570740911}{258788222000}e^{5} - \frac{5365059234251}{129394111000}e^{3} + \frac{18759762961}{1293941110}e$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{18138487}{517576444000}e^{13} - \frac{10312259}{3696974600}e^{11} + \frac{4334450891}{51757644400}e^{9} - \frac{152911891787}{129394111000}e^{7} + \frac{4070153211227}{517576444000}e^{5} - \frac{673377117629}{32348527750}e^{3} + \frac{5726657301}{646970555}e$
29 $[29, 29, -w^{5} - w^{4} + 5w^{3} + 2w^{2} - 3w - 1]$ $\phantom{-}\frac{2173193}{23526202000}e^{13} - \frac{2512247}{336088600}e^{11} + \frac{270791037}{1176310100}e^{9} - \frac{39700825911}{11763101000}e^{7} + \frac{557289537403}{23526202000}e^{5} - \frac{97524144706}{1470387625}e^{3} + \frac{282879291}{11763101}e$
41 $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$ $\phantom{-}1$
41 $[41, 41, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 5]$ $-\frac{1256023}{12939411100}e^{12} + \frac{5487073}{739394920}e^{10} - \frac{1087287321}{5175764440}e^{8} + \frac{70179055759}{25878822200}e^{6} - \frac{405707808141}{25878822200}e^{4} + \frac{433990288231}{12939411100}e^{2} - \frac{1592357587}{129394111}$
43 $[43, 43, -w^{2} - w + 2]$ $-\frac{32596947}{258788222000}e^{13} + \frac{37166953}{3696974600}e^{11} - \frac{3939497823}{12939411100}e^{9} + \frac{566767240869}{129394111000}e^{7} - \frac{7815916594737}{258788222000}e^{5} + \frac{1363678718349}{16174263875}e^{3} - \frac{24719138354}{646970555}e$
43 $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 5]$ $\phantom{-}\frac{9812007}{73939492000}e^{13} - \frac{79289141}{7393949200}e^{11} + \frac{1219790313}{3696974600}e^{9} - \frac{179057470239}{36969746000}e^{7} + \frac{2534582288597}{73939492000}e^{5} - \frac{458346596019}{4621218250}e^{3} + \frac{8956750821}{184848730}e$
43 $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$ $-\frac{12902423}{258788222000}e^{13} + \frac{14741477}{3696974600}e^{11} - \frac{3123921489}{25878822200}e^{9} + \frac{55838532749}{32348527750}e^{7} - \frac{3021569360783}{258788222000}e^{5} + \frac{3986299028653}{129394111000}e^{3} - \frac{5922617861}{646970555}e$
43 $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 15w + 3]$ $\phantom{-}\frac{14339041}{517576444000}e^{13} - \frac{4232011}{1848487300}e^{11} + \frac{3753570563}{51757644400}e^{9} - \frac{17864089352}{16174263875}e^{7} + \frac{4244245590961}{517576444000}e^{5} - \frac{1683866101419}{64697055500}e^{3} + \frac{29878064603}{1293941110}e$
49 $[49, 7, -w^{5} - w^{4} + 6w^{3} + 3w^{2} - 7w]$ $\phantom{-}\frac{189199}{5175764440}e^{12} - \frac{96137}{36969746}e^{10} + \frac{17073291}{258788222}e^{8} - \frac{466657732}{646970555}e^{6} + \frac{17263211789}{5175764440}e^{4} - \frac{8998927227}{1293941110}e^{2} + \frac{1092851794}{129394111}$
71 $[71, 71, -5w^{5} - 2w^{4} + 32w^{3} - w^{2} - 35w - 2]$ $-\frac{2053571}{25878822200}e^{12} + \frac{4688093}{739394920}e^{10} - \frac{978738361}{5175764440}e^{8} + \frac{67126029109}{25878822200}e^{6} - \frac{103661989979}{6469705550}e^{4} + \frac{111753877614}{3234852775}e^{2} + \frac{118985190}{129394111}$
71 $[71, 71, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 6]$ $\phantom{-}\frac{3055161}{129394111000}e^{13} - \frac{3528739}{1848487300}e^{11} + \frac{1492768821}{25878822200}e^{9} - \frac{103295152119}{129394111000}e^{7} + \frac{312197871903}{64697055500}e^{5} - \frac{1049467339167}{129394111000}e^{3} - \frac{6951284771}{646970555}e$
71 $[71, 71, -3w^{5} - 2w^{4} + 19w^{3} + 5w^{2} - 22w - 7]$ $-\frac{2122497}{258788222000}e^{13} + \frac{6515281}{7393949200}e^{11} - \frac{1810338317}{51757644400}e^{9} + \frac{165575281813}{258788222000}e^{7} - \frac{702233168831}{129394111000}e^{5} + \frac{588793863773}{32348527750}e^{3} - \frac{8694619189}{646970555}e$
71 $[71, 71, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 6]$ $-\frac{1009537}{51757644400}e^{12} + \frac{2311871}{1478789840}e^{10} - \frac{481524027}{10351528880}e^{8} + \frac{32784198123}{51757644400}e^{6} - \frac{25754158019}{6469705550}e^{4} + \frac{67898928183}{6469705550}e^{2} - \frac{32793696}{129394111}$
83 $[83, 83, -2w^{5} - w^{4} + 12w^{3} - 12w + 1]$ $\phantom{-}\frac{210103}{1848487300}e^{12} - \frac{1702629}{184848730}e^{10} + \frac{52556359}{184848730}e^{8} - \frac{7738487137}{1848487300}e^{6} + \frac{54677852463}{1848487300}e^{4} - \frac{153392720741}{1848487300}e^{2} + \frac{482931175}{18484873}$
83 $[83, 83, -2w^{5} - w^{4} + 13w^{3} - 16w + 1]$ $-\frac{23421}{2070305776}e^{12} + \frac{485297}{295757968}e^{10} - \frac{157755009}{2070305776}e^{8} + \frac{3158231913}{2070305776}e^{6} - \frac{14068257985}{1035152888}e^{4} + \frac{5724450884}{129394111}e^{2} - \frac{901598924}{129394111}$
83 $[83, 83, -4w^{5} - 2w^{4} + 26w^{3} + 3w^{2} - 29w - 6]$ $-\frac{3929633}{51757644400}e^{12} + \frac{2374461}{369697460}e^{10} - \frac{1063396269}{5175764440}e^{8} + \frac{39723872733}{12939411100}e^{6} - \frac{1093506580093}{51757644400}e^{4} + \frac{174530622086}{3234852775}e^{2} - \frac{1743066769}{129394111}$
83 $[83, 83, 2w^{5} - 13w^{3} + 5w^{2} + 13w - 1]$ $\phantom{-}4$
97 $[97, 97, -3w^{5} + 20w^{3} - 8w^{2} - 22w + 5]$ $-\frac{373899}{12939411100}e^{13} + \frac{3502029}{1478789840}e^{11} - \frac{762669101}{10351528880}e^{9} + \frac{56150128459}{51757644400}e^{7} - \frac{390913596131}{51757644400}e^{5} + \frac{508568353511}{25878822200}e^{3} + \frac{3680866031}{646970555}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$41$ $[41,41,-2w^{5}+13w^{3}-4w^{2}-12w]$ $-1$