# Properties

 Base field 3.3.1101.1 Weight [2, 2, 2] Level norm 16 Level $[16, 4, -w^{2} + w + 5]$ Label 3.3.1101.1-16.2-b Dimension 11 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1101.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 9x + 12$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[16, 4, -w^{2} + w + 5]$ Label 3.3.1101.1-16.2-b Dimension 11 Is CM no Is base change no Parent newspace dimension 26

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{11}$$ $$\mathstrut +\mathstrut 2x^{10}$$ $$\mathstrut -\mathstrut 18x^{9}$$ $$\mathstrut -\mathstrut 34x^{8}$$ $$\mathstrut +\mathstrut 116x^{7}$$ $$\mathstrut +\mathstrut 207x^{6}$$ $$\mathstrut -\mathstrut 316x^{5}$$ $$\mathstrut -\mathstrut 552x^{4}$$ $$\mathstrut +\mathstrut 291x^{3}$$ $$\mathstrut +\mathstrut 591x^{2}$$ $$\mathstrut +\mathstrut 39x$$ $$\mathstrut -\mathstrut 99$$
Norm Prime Eigenvalue
2 $[2, 2, w - 2]$ $\phantom{-}e$
3 $[3, 3, -w + 3]$ $\phantom{-}\frac{14}{383}e^{10} - \frac{115}{383}e^{9} - \frac{582}{383}e^{8} + \frac{1584}{383}e^{7} + \frac{6236}{383}e^{6} - \frac{6467}{383}e^{5} - \frac{24680}{383}e^{4} + \frac{6244}{383}e^{3} + \frac{34131}{383}e^{2} + \frac{7168}{383}e - \frac{6411}{383}$
3 $[3, 3, w - 1]$ $\phantom{-}\frac{163}{1149}e^{10} + \frac{494}{1149}e^{9} - \frac{672}{383}e^{8} - \frac{6781}{1149}e^{7} + \frac{5744}{1149}e^{6} + \frac{9381}{383}e^{5} + \frac{7619}{1149}e^{4} - \frac{11131}{383}e^{3} - \frac{12450}{383}e^{2} - \frac{2949}{383}e + \frac{2066}{383}$
4 $[4, 2, w^{2} + w - 7]$ $\phantom{-}0$
19 $[19, 19, w + 1]$ $-\frac{205}{1149}e^{10} - \frac{149}{1149}e^{9} + \frac{1254}{383}e^{8} + \frac{2029}{1149}e^{7} - \frac{24452}{1149}e^{6} - \frac{2914}{383}e^{5} + \frac{66421}{1149}e^{4} + \frac{4504}{383}e^{3} - \frac{22064}{383}e^{2} - \frac{2687}{383}e + \frac{5111}{383}$
23 $[23, 23, w^{2} - 2w - 1]$ $\phantom{-}\frac{119}{383}e^{10} - \frac{20}{383}e^{9} - \frac{2649}{383}e^{8} + \frac{59}{383}e^{7} + \frac{20834}{383}e^{6} + \frac{1906}{383}e^{5} - \frac{68453}{383}e^{4} - \frac{12419}{383}e^{3} + \frac{83868}{383}e^{2} + \frac{22628}{383}e - \frac{19449}{383}$
31 $[31, 31, -2w^{2} + 19]$ $-\frac{103}{1149}e^{10} - \frac{1151}{1149}e^{9} - \frac{433}{383}e^{8} + \frac{16360}{1149}e^{7} + \frac{33949}{1149}e^{6} - \frac{23708}{383}e^{5} - \frac{178391}{1149}e^{4} + \frac{28094}{383}e^{3} + \frac{96554}{383}e^{2} + \frac{17785}{383}e - \frac{18994}{383}$
31 $[31, 31, -w^{2} + 5]$ $\phantom{-}\frac{794}{1149}e^{10} + \frac{2068}{1149}e^{9} - \frac{3835}{383}e^{8} - \frac{29387}{1149}e^{7} + \frac{53836}{1149}e^{6} + \frac{44202}{383}e^{5} - \frac{91490}{1149}e^{4} - \frac{69501}{383}e^{3} + \frac{12796}{383}e^{2} + \frac{21886}{383}e - \frac{6955}{383}$
31 $[31, 31, -3w + 5]$ $\phantom{-}\frac{794}{1149}e^{10} + \frac{2068}{1149}e^{9} - \frac{3835}{383}e^{8} - \frac{29387}{1149}e^{7} + \frac{52687}{1149}e^{6} + \frac{43819}{383}e^{5} - \frac{77702}{1149}e^{4} - \frac{66054}{383}e^{3} - \frac{1758}{383}e^{2} + \frac{16141}{383}e + \frac{1471}{383}$
41 $[41, 41, w^{2} + 2w - 7]$ $-\frac{259}{383}e^{10} - \frac{745}{383}e^{9} + \frac{3490}{383}e^{8} + \frac{10528}{383}e^{7} - \frac{13488}{383}e^{6} - \frac{46774}{383}e^{5} + \frac{9236}{383}e^{4} + \frac{69475}{383}e^{3} + \frac{24081}{383}e^{2} - \frac{12729}{383}e - \frac{6063}{383}$
43 $[43, 43, w^{2} - 11]$ $-\frac{763}{1149}e^{10} - \frac{818}{1149}e^{9} + \frac{4828}{383}e^{8} + \frac{12103}{1149}e^{7} - \frac{99338}{1149}e^{6} - \frac{19694}{383}e^{5} + \frac{292576}{1149}e^{4} + \frac{38363}{383}e^{3} - \frac{108167}{383}e^{2} - \frac{32426}{383}e + \frac{23972}{383}$
47 $[47, 47, 3w - 7]$ $-\frac{52}{383}e^{10} - \frac{503}{383}e^{9} - \frac{191}{383}e^{8} + \frac{7248}{383}e^{7} + \frac{10104}{383}e^{6} - \frac{32609}{383}e^{5} - \frac{56443}{383}e^{4} + \frac{45365}{383}e^{3} + \frac{94164}{383}e^{2} + \frac{5931}{383}e - \frac{20178}{383}$
53 $[53, 53, -3w^{2} - 6w + 11]$ $-\frac{160}{383}e^{10} - \frac{546}{383}e^{9} + \frac{1946}{383}e^{8} + \frac{7777}{383}e^{7} - \frac{5119}{383}e^{6} - \frac{34371}{383}e^{5} - \frac{10336}{383}e^{4} + \frac{46987}{383}e^{3} + \frac{42612}{383}e^{2} + \frac{2340}{383}e - \frac{10116}{383}$
59 $[59, 59, 2w - 1]$ $-\frac{109}{383}e^{10} - \frac{281}{383}e^{9} + \frac{1522}{383}e^{8} + \frac{4027}{383}e^{7} - \frac{6367}{383}e^{6} - \frac{18453}{383}e^{5} + \frac{6670}{383}e^{4} + \frac{29518}{383}e^{3} + \frac{5676}{383}e^{2} - \frac{8699}{383}e - \frac{888}{383}$
67 $[67, 67, 2w^{2} + w - 19]$ $\phantom{-}\frac{431}{1149}e^{10} + \frac{1849}{1149}e^{9} - \frac{1650}{383}e^{8} - \frac{26960}{1149}e^{7} + \frac{10000}{1149}e^{6} + \frac{41469}{383}e^{5} + \frac{42703}{1149}e^{4} - \frac{63336}{383}e^{3} - \frac{43557}{383}e^{2} + \frac{9724}{383}e + \frac{4765}{383}$
67 $[67, 67, 3w^{2} + 2w - 25]$ $\phantom{-}\frac{695}{1149}e^{10} + \frac{1486}{1149}e^{9} - \frac{3448}{383}e^{8} - \frac{20891}{1149}e^{7} + \frac{50446}{1149}e^{6} + \frac{31131}{383}e^{5} - \frac{91451}{1149}e^{4} - \frac{49366}{383}e^{3} + \frac{14279}{383}e^{2} + \frac{17629}{383}e - \frac{4072}{383}$
67 $[67, 67, w - 5]$ $-\frac{157}{1149}e^{10} - \frac{215}{1149}e^{9} + \frac{1136}{383}e^{8} + \frac{4177}{1149}e^{7} - \frac{26708}{1149}e^{6} - \frac{9320}{383}e^{5} + \frac{89974}{1149}e^{4} + \frac{25045}{383}e^{3} - \frac{38428}{383}e^{2} - \frac{23603}{383}e + \frac{7961}{383}$
73 $[73, 73, -4w^{2} - 3w + 29]$ $\phantom{-}\frac{200}{1149}e^{10} + \frac{874}{1149}e^{9} - \frac{747}{383}e^{8} - \frac{12881}{1149}e^{7} + \frac{3622}{1149}e^{6} + \frac{19779}{383}e^{5} + \frac{25942}{1149}e^{4} - \frac{27589}{383}e^{3} - \frac{23883}{383}e^{2} - \frac{3656}{383}e + \frac{1151}{383}$
73 $[73, 73, 2w^{2} - w - 11]$ $-\frac{418}{1149}e^{10} - \frac{287}{1149}e^{9} + \frac{2783}{383}e^{8} + \frac{4849}{1149}e^{7} - \frac{59252}{1149}e^{6} - \frac{9484}{383}e^{5} + \frac{174685}{1149}e^{4} + \frac{23011}{383}e^{3} - \frac{61572}{383}e^{2} - \frac{22187}{383}e + \frac{12428}{383}$
73 $[73, 73, w^{2} + 2w - 11]$ $-\frac{937}{1149}e^{10} - \frac{2015}{1149}e^{9} + \frac{5160}{383}e^{8} + \frac{30169}{1149}e^{7} - \frac{88862}{1149}e^{6} - \frac{49039}{383}e^{5} + \frac{209638}{1149}e^{4} + \frac{87180}{383}e^{3} - \frac{58231}{383}e^{2} - \frac{41057}{383}e + \frac{15460}{383}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w^{2} + w - 7]$ $1$