# Properties

 Base field 3.3.1849.1 Weight [2, 2, 2] Level norm 8 Level $[8,8,w^{2} - 2w - 11]$ Label 3.3.1849.1-8.9-c Dimension 11 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1849.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 14x - 8$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[8,8,w^{2} - 2w - 11]$ Label 3.3.1849.1-8.9-c Dimension 11 Is CM no Is base change no Parent newspace dimension 18

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{11} - 17x^{9} + 2x^{8} + 100x^{7} - 21x^{6} - 240x^{5} + 63x^{4} + 215x^{3} - 57x^{2} - 37x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{2}w^{2} + \frac{1}{2}w + 8]$ $\phantom{-}e$
2 $[2, 2, \frac{1}{2}w^{2} - \frac{3}{2}w - 1]$ $-\frac{47}{2521}e^{10} + \frac{85}{2521}e^{9} + \frac{538}{2521}e^{8} - \frac{1657}{2521}e^{7} - \frac{1006}{2521}e^{6} + \frac{10423}{2521}e^{5} - \frac{4620}{2521}e^{4} - \frac{23624}{2521}e^{3} + \frac{10413}{2521}e^{2} + \frac{14689}{2521}e - \frac{1279}{2521}$
2 $[2, 2, w + 3]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 3w + 7]$ $-\frac{749}{2521}e^{10} + \frac{550}{2521}e^{9} + \frac{12972}{2521}e^{8} - \frac{9832}{2521}e^{7} - \frac{77394}{2521}e^{6} + \frac{55876}{2521}e^{5} + \frac{186467}{2521}e^{4} - \frac{111932}{2521}e^{3} - \frac{161143}{2521}e^{2} + \frac{66574}{2521}e + \frac{17379}{2521}$
11 $[11, 11, -2w - 1]$ $\phantom{-}\frac{37}{2521}e^{10} + \frac{94}{2521}e^{9} - \frac{799}{2521}e^{8} - \frac{1002}{2521}e^{7} + \frac{7014}{2521}e^{6} + \frac{1235}{2521}e^{5} - \frac{27205}{2521}e^{4} + \frac{11571}{2521}e^{3} + \frac{35035}{2521}e^{2} - \frac{20414}{2521}e + \frac{2026}{2521}$
11 $[11, 11, -w^{2} + w + 11]$ $\phantom{-}\frac{540}{2521}e^{10} + \frac{418}{2521}e^{9} - \frac{8595}{2521}e^{8} - \frac{5153}{2521}e^{7} + \frac{46155}{2521}e^{6} + \frac{18365}{2521}e^{5} - \frac{96570}{2521}e^{4} - \frac{12161}{2521}e^{3} + \frac{69329}{2521}e^{2} - \frac{21101}{2521}e - \frac{2523}{2521}$
27 $[27, 3, 3]$ $-\frac{250}{2521}e^{10} - \frac{567}{2521}e^{9} + \frac{3559}{2521}e^{8} + \frac{9155}{2521}e^{7} - \frac{16186}{2521}e^{6} - \frac{51406}{2521}e^{5} + \frac{26221}{2521}e^{4} + \frac{114640}{2521}e^{3} - \frac{13376}{2521}e^{2} - \frac{75058}{2521}e + \frac{1028}{2521}$
41 $[41, 41, 2w + 5]$ $-\frac{12}{2521}e^{10} + \frac{719}{2521}e^{9} + \frac{191}{2521}e^{8} - \frac{11258}{2521}e^{7} + \frac{655}{2521}e^{6} + \frac{57855}{2521}e^{5} - \frac{12980}{2521}e^{4} - \frac{108749}{2521}e^{3} + \frac{27815}{2521}e^{2} + \frac{61197}{2521}e + \frac{2409}{2521}$
41 $[41, 41, -w^{2} + 3w + 3]$ $\phantom{-}\frac{1661}{2521}e^{10} + \frac{268}{2521}e^{9} - \frac{27488}{2521}e^{8} - \frac{1784}{2521}e^{7} + \frac{153664}{2521}e^{6} - \frac{770}{2521}e^{5} - \frac{331916}{2521}e^{4} + \frac{12178}{2521}e^{3} + \frac{235431}{2521}e^{2} - \frac{13360}{2521}e - \frac{16430}{2521}$
41 $[41, 41, -w^{2} + w + 15]$ $\phantom{-}\frac{1491}{2521}e^{10} + \frac{790}{2521}e^{9} - \frac{24362}{2521}e^{8} - \frac{9172}{2521}e^{7} + \frac{134792}{2521}e^{6} + \frac{31030}{2521}e^{5} - \frac{290590}{2521}e^{4} - \frac{28858}{2521}e^{3} + \frac{211411}{2521}e^{2} - \frac{7324}{2521}e - \frac{11294}{2521}$
43 $[43, 43, -3w^{2} + 11w + 11]$ $\phantom{-}\frac{1324}{2521}e^{10} + \frac{502}{2521}e^{9} - \frac{21914}{2521}e^{8} - \frac{4922}{2521}e^{7} + \frac{125210}{2521}e^{6} + \frac{9921}{2521}e^{5} - \frac{291397}{2521}e^{4} + \frac{12125}{2521}e^{3} + \frac{252916}{2521}e^{2} - \frac{28562}{2521}e - \frac{28819}{2521}$
47 $[47, 47, -w^{2} - w + 5]$ $\phantom{-}\frac{665}{2521}e^{10} - \frac{559}{2521}e^{9} - \frac{11635}{2521}e^{8} + \frac{9177}{2521}e^{7} + \frac{69374}{2521}e^{6} - \frac{49209}{2521}e^{5} - \frac{163882}{2521}e^{4} + \frac{96905}{2521}e^{3} + \frac{136521}{2521}e^{2} - \frac{59202}{2521}e - \frac{18163}{2521}$
47 $[47, 47, w^{2} - 5w - 3]$ $\phantom{-}\frac{124}{2521}e^{10} - \frac{707}{2521}e^{9} - \frac{2814}{2521}e^{8} + \frac{11291}{2521}e^{7} + \frac{21803}{2521}e^{6} - \frac{60862}{2521}e^{5} - \frac{71755}{2521}e^{4} + \frac{126264}{2521}e^{3} + \frac{97451}{2521}e^{2} - \frac{85312}{2521}e - \frac{19851}{2521}$
47 $[47, 47, -2w^{2} + 4w + 23]$ $\phantom{-}\frac{1453}{2521}e^{10} + \frac{966}{2521}e^{9} - \frac{23337}{2521}e^{8} - \frac{11209}{2521}e^{7} + \frac{126362}{2521}e^{6} + \frac{36507}{2521}e^{5} - \frac{260265}{2521}e^{4} - \frac{23231}{2521}e^{3} + \frac{156215}{2521}e^{2} - \frac{24037}{2521}e + \frac{10200}{2521}$
59 $[59, 59, -w^{2} + w + 13]$ $-\frac{591}{2521}e^{10} + \frac{747}{2521}e^{9} + \frac{10037}{2521}e^{8} - \frac{13702}{2521}e^{7} - \frac{57867}{2521}e^{6} + \frac{81931}{2521}e^{5} + \frac{132161}{2521}e^{4} - \frac{179645}{2521}e^{3} - \frac{109308}{2521}e^{2} + \frac{121735}{2521}e + \frac{9610}{2521}$
59 $[59, 59, w^{2} - 3w - 5]$ $\phantom{-}\frac{65}{2521}e^{10} + \frac{97}{2521}e^{9} + \frac{436}{2521}e^{8} - \frac{1624}{2521}e^{7} - \frac{16363}{2521}e^{6} + \frac{12458}{2521}e^{5} + \frac{87115}{2521}e^{4} - \frac{48966}{2521}e^{3} - \frac{118942}{2521}e^{2} + \frac{68725}{2521}e + \frac{11531}{2521}$
59 $[59, 59, -2w - 3]$ $\phantom{-}\frac{2105}{2521}e^{10} + \frac{1396}{2521}e^{9} - \frac{34555}{2521}e^{8} - \frac{16329}{2521}e^{7} + \frac{194975}{2521}e^{6} + \frac{51865}{2521}e^{5} - \frac{441570}{2521}e^{4} - \frac{17877}{2521}e^{3} + \frac{350810}{2521}e^{2} - \frac{69253}{2521}e - \frac{24891}{2521}$
97 $[97, 97, 7w^{2} - 11w - 91]$ $-\frac{2464}{2521}e^{10} - \frac{264}{2521}e^{9} + \frac{40059}{2521}e^{8} - \frac{726}{2521}e^{7} - \frac{219287}{2521}e^{6} + \frac{25818}{2521}e^{5} + \frac{462494}{2521}e^{4} - \frac{82810}{2521}e^{3} - \frac{323087}{2521}e^{2} + \frac{81792}{2521}e + \frac{23221}{2521}$
97 $[97, 97, -2w^{2} - 8w - 5]$ $\phantom{-}\frac{946}{2521}e^{10} + \frac{1722}{2521}e^{9} - \frac{14637}{2521}e^{8} - \frac{24256}{2521}e^{7} + \frac{76515}{2521}e^{6} + \frac{109250}{2521}e^{5} - \frac{153210}{2521}e^{4} - \frac{170202}{2521}e^{3} + \frac{81613}{2521}e^{2} + \frac{75200}{2521}e + \frac{28157}{2521}$
97 $[97, 97, 5w^{2} - 19w - 15]$ $-\frac{1446}{2521}e^{10} - \frac{335}{2521}e^{9} + \frac{21755}{2521}e^{8} + \frac{2230}{2521}e^{7} - \frac{103845}{2521}e^{6} - \frac{298}{2521}e^{5} + \frac{162795}{2521}e^{4} - \frac{3878}{2521}e^{3} - \frac{42819}{2521}e^{2} - \frac{5989}{2521}e - \frac{23580}{2521}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2,2,w + 3]$ $-1$