# Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 29 Level $[29, 29, w^{2} - w - 8]$ Label 4.4.11525.1-29.1-b Dimension 10 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.11525.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 11x^{2} + 5x + 25$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[29, 29, w^{2} - w - 8]$ Label 4.4.11525.1-29.1-b Dimension 10 Is CM no Is base change no Parent newspace dimension 28

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{10}$$ $$\mathstrut +\mathstrut x^{9}$$ $$\mathstrut -\mathstrut 17x^{8}$$ $$\mathstrut -\mathstrut 19x^{7}$$ $$\mathstrut +\mathstrut 92x^{6}$$ $$\mathstrut +\mathstrut 119x^{5}$$ $$\mathstrut -\mathstrut 154x^{4}$$ $$\mathstrut -\mathstrut 255x^{3}$$ $$\mathstrut -\mathstrut 23x^{2}$$ $$\mathstrut +\mathstrut 64x$$ $$\mathstrut +\mathstrut 12$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-\frac{3471}{9323}e^{9} - \frac{723}{9323}e^{8} + \frac{58967}{9323}e^{7} + \frac{19450}{9323}e^{6} - \frac{324626}{9323}e^{5} - \frac{156219}{9323}e^{4} + \frac{607980}{9323}e^{3} + \frac{388375}{9323}e^{2} - \frac{161336}{9323}e - \frac{61038}{9323}$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{5003}{9323}e^{9} + \frac{470}{9323}e^{8} - \frac{85270}{9323}e^{7} - \frac{17041}{9323}e^{6} + \frac{473711}{9323}e^{5} + \frac{157878}{9323}e^{4} - \frac{908613}{9323}e^{3} - \frac{431645}{9323}e^{2} + \frac{265279}{9323}e + \frac{69969}{9323}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{626}{9323}e^{9} + \frac{493}{9323}e^{8} - \frac{11685}{9323}e^{7} - \frac{7937}{9323}e^{6} + \frac{71982}{9323}e^{5} + \frac{42461}{9323}e^{4} - \frac{159174}{9323}e^{3} - \frac{75980}{9323}e^{2} + \frac{85473}{9323}e - \frac{7122}{9323}$
16 $[16, 2, 2]$ $-\frac{2725}{9323}e^{9} - \frac{761}{9323}e^{8} + \frac{46025}{9323}e^{7} + \frac{15353}{9323}e^{6} - \frac{253113}{9323}e^{5} - \frac{104159}{9323}e^{4} + \frac{485699}{9323}e^{3} + \frac{241773}{9323}e^{2} - \frac{175167}{9323}e - \frac{47573}{9323}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{3528}{9323}e^{9} + \frac{1170}{9323}e^{8} - \frac{59331}{9323}e^{7} - \frac{26949}{9323}e^{6} + \frac{323704}{9323}e^{5} + \frac{196439}{9323}e^{4} - \frac{597215}{9323}e^{3} - \frac{457814}{9323}e^{2} + \frac{121625}{9323}e + \frac{58930}{9323}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{2019}{9323}e^{9} - \frac{622}{9323}e^{8} + \frac{33502}{9323}e^{7} + \frac{9976}{9323}e^{6} - \frac{178336}{9323}e^{5} - \frac{52191}{9323}e^{4} + \frac{316936}{9323}e^{3} + \frac{96958}{9323}e^{2} - \frac{78205}{9323}e - \frac{16109}{9323}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{5793}{9323}e^{9} - \frac{695}{9323}e^{8} - \frac{95876}{9323}e^{7} - \frac{1084}{9323}e^{6} + \frac{511800}{9323}e^{5} + \frac{94434}{9323}e^{4} - \frac{936878}{9323}e^{3} - \frac{366716}{9323}e^{2} + \frac{288999}{9323}e + \frac{85078}{9323}$
19 $[19, 19, w - 1]$ $-\frac{5013}{9323}e^{9} + \frac{1905}{9323}e^{8} + \frac{83044}{9323}e^{7} - \frac{20571}{9323}e^{6} - \frac{444926}{9323}e^{5} + \frac{28559}{9323}e^{4} + \frac{827070}{9323}e^{3} + \frac{131425}{9323}e^{2} - \frac{291188}{9323}e - \frac{21185}{9323}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}1$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $-\frac{3075}{9323}e^{9} - \frac{1543}{9323}e^{8} + \frac{52022}{9323}e^{7} + \frac{32122}{9323}e^{6} - \frac{280491}{9323}e^{5} - \frac{216840}{9323}e^{4} + \frac{484532}{9323}e^{3} + \frac{492815}{9323}e^{2} - \frac{47129}{9323}e - \frac{102180}{9323}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{386}{9323}e^{9} - \frac{1555}{9323}e^{8} + \frac{9171}{9323}e^{7} + \frac{24940}{9323}e^{6} - \frac{72920}{9323}e^{5} - \frac{125816}{9323}e^{4} + \frac{214314}{9323}e^{3} + \frac{205103}{9323}e^{2} - \frac{162882}{9323}e - \frac{54257}{9323}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{2891}{9323}e^{9} - \frac{1372}{9323}e^{8} - \frac{48230}{9323}e^{7} + \frac{17928}{9323}e^{6} + \frac{260078}{9323}e^{5} - \frac{59544}{9323}e^{4} - \frac{489514}{9323}e^{3} + \frac{24441}{9323}e^{2} + \frac{206232}{9323}e - \frac{46235}{9323}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}\frac{1360}{9323}e^{9} + \frac{3305}{9323}e^{8} - \frac{23569}{9323}e^{7} - \frac{49710}{9323}e^{6} + \frac{131422}{9323}e^{5} + \frac{226880}{9323}e^{4} - \frac{237597}{9323}e^{3} - \frac{321802}{9323}e^{2} + \frac{36822}{9323}e + \frac{59290}{9323}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}\frac{15359}{9323}e^{9} + \frac{2192}{9323}e^{8} - \frac{261807}{9323}e^{7} - \frac{67892}{9323}e^{6} + \frac{1448511}{9323}e^{5} + \frac{586315}{9323}e^{4} - \frac{2743318}{9323}e^{3} - \frac{1545977}{9323}e^{2} + \frac{779675}{9323}e + \frac{292483}{9323}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{5433}{9323}e^{9} + \frac{898}{9323}e^{8} - \frac{92105}{9323}e^{7} - \frac{21927}{9323}e^{6} + \frac{503884}{9323}e^{5} + \frac{168190}{9323}e^{4} - \frac{935681}{9323}e^{3} - \frac{406571}{9323}e^{2} + \frac{279252}{9323}e - \frac{4652}{9323}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}\frac{5203}{9323}e^{9} - \frac{415}{9323}e^{8} - \frac{87365}{9323}e^{7} - \frac{1318}{9323}e^{6} + \frac{476037}{9323}e^{5} + \frac{74431}{9323}e^{4} - \frac{890632}{9323}e^{3} - \frac{300735}{9323}e^{2} + \frac{252048}{9323}e + \frac{17266}{9323}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $-\frac{189}{9323}e^{9} + \frac{2934}{9323}e^{8} + \frac{2679}{9323}e^{7} - \frac{52663}{9323}e^{6} - \frac{20005}{9323}e^{5} + \frac{306292}{9323}e^{4} + \frac{108076}{9323}e^{3} - \frac{593123}{9323}e^{2} - \frac{240756}{9323}e + \frac{99729}{9323}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}\frac{1859}{9323}e^{9} + \frac{1330}{9323}e^{8} - \frac{31826}{9323}e^{7} - \frac{24419}{9323}e^{6} + \frac{172746}{9323}e^{5} + \frac{154376}{9323}e^{4} - \frac{288435}{9323}e^{3} - \frac{350854}{9323}e^{2} - \frac{28680}{9323}e + \frac{97428}{9323}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{3620}{9323}e^{9} - \frac{2034}{9323}e^{8} - \frac{61227}{9323}e^{7} + \frac{22610}{9323}e^{6} + \frac{338572}{9323}e^{5} - \frac{38289}{9323}e^{4} - \frac{669308}{9323}e^{3} - \frac{138416}{9323}e^{2} + \frac{307779}{9323}e + \frac{72538}{9323}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
29 $[29, 29, w^{2} - w - 8]$ $-1$