# Properties

 Base field 4.4.18625.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ Label 4.4.18625.1-11.1-e Dimension 14 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18625.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 9x + 41$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ Label 4.4.18625.1-11.1-e Dimension 14 Is CM no Is base change no Parent newspace dimension 20

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{14}$$ $$\mathstrut -\mathstrut 37x^{12}$$ $$\mathstrut +\mathstrut 527x^{10}$$ $$\mathstrut -\mathstrut 3683x^{8}$$ $$\mathstrut +\mathstrut 13435x^{6}$$ $$\mathstrut -\mathstrut 24687x^{4}$$ $$\mathstrut +\mathstrut 18629x^{2}$$ $$\mathstrut -\mathstrut 1369$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $\phantom{-}e$
4 $[4, 2, w - 3]$ $-\frac{5897}{36704}e^{13} + \frac{343}{62}e^{11} - \frac{2586463}{36704}e^{9} + \frac{1884593}{4588}e^{7} - \frac{40499627}{36704}e^{5} + \frac{1299314}{1147}e^{3} - \frac{3380165}{36704}e$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $-\frac{2869}{18352}e^{13} + \frac{333}{62}e^{11} - \frac{1251483}{18352}e^{9} + \frac{453830}{1147}e^{7} - \frac{19384047}{18352}e^{5} + \frac{1233849}{1147}e^{3} - \frac{1540633}{18352}e$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $-\frac{4459}{36704}e^{13} + \frac{1035}{248}e^{11} - \frac{1944225}{36704}e^{9} + \frac{1408841}{4588}e^{7} - \frac{30019249}{36704}e^{5} + \frac{7588405}{9176}e^{3} - \frac{2010811}{36704}e$
9 $[9, 3, -w - 2]$ $\phantom{-}\frac{1287}{18352}e^{13} - \frac{599}{248}e^{11} + \frac{564659}{18352}e^{9} - \frac{205599}{1147}e^{7} + \frac{8808669}{18352}e^{5} - \frac{4452733}{9176}e^{3} + \frac{442265}{18352}e$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $-1$
11 $[11, 11, -w + 2]$ $-\frac{205}{992}e^{12} + \frac{220}{31}e^{10} - \frac{89331}{992}e^{8} + \frac{64733}{124}e^{6} - \frac{1380439}{992}e^{4} + \frac{87493}{62}e^{2} - \frac{100449}{992}$
41 $[41, 41, -w]$ $-\frac{383}{992}e^{12} + \frac{3295}{248}e^{10} - \frac{167733}{992}e^{8} + \frac{122045}{124}e^{6} - \frac{2616477}{992}e^{4} + \frac{668485}{248}e^{2} - \frac{205607}{992}$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $\phantom{-}\frac{401}{992}e^{12} - \frac{3445}{248}e^{10} + \frac{175019}{992}e^{8} - \frac{127013}{124}e^{6} + \frac{2715555}{992}e^{4} - \frac{692227}{248}e^{2} + \frac{213545}{992}$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $-\frac{15957}{36704}e^{13} + \frac{1851}{124}e^{11} - \frac{6950947}{36704}e^{9} + \frac{5036687}{4588}e^{7} - \frac{107529551}{36704}e^{5} + \frac{13749765}{4588}e^{3} - \frac{9847249}{36704}e$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $-\frac{1287}{9176}e^{13} + \frac{599}{124}e^{11} - \frac{564659}{9176}e^{9} + \frac{411198}{1147}e^{7} - \frac{8808669}{9176}e^{5} + \frac{4457321}{4588}e^{3} - \frac{524849}{9176}e$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}\frac{49}{62}e^{12} - \frac{1685}{62}e^{10} + \frac{10711}{31}e^{8} - \frac{124529}{62}e^{6} + \frac{166626}{31}e^{4} - \frac{170027}{31}e^{2} + \frac{25701}{62}$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $\phantom{-}\frac{49}{62}e^{12} - \frac{1685}{62}e^{10} + \frac{10711}{31}e^{8} - \frac{124529}{62}e^{6} + \frac{166626}{31}e^{4} - \frac{170027}{31}e^{2} + \frac{25701}{62}$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $-\frac{79}{992}e^{12} + \frac{679}{248}e^{10} - \frac{34485}{992}e^{8} + \frac{24997}{124}e^{6} - \frac{534125}{992}e^{4} + \frac{137061}{248}e^{2} - \frac{40295}{992}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $-\frac{107}{496}e^{12} + \frac{1835}{248}e^{10} - \frac{46487}{496}e^{8} + \frac{33593}{62}e^{6} - \frac{713129}{496}e^{4} + \frac{359177}{248}e^{2} - \frac{50597}{496}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $-\frac{205}{992}e^{12} + \frac{220}{31}e^{10} - \frac{89331}{992}e^{8} + \frac{64733}{124}e^{6} - \frac{1380439}{992}e^{4} + \frac{87555}{62}e^{2} - \frac{105409}{992}$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $-\frac{143}{496}e^{12} + \frac{1233}{124}e^{10} - \frac{62981}{496}e^{8} + \frac{46071}{62}e^{6} - \frac{995357}{496}e^{4} + \frac{256135}{124}e^{2} - \frac{72487}{496}$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $-\frac{3437}{9176}e^{13} + \frac{797}{62}e^{11} - \frac{1495023}{9176}e^{9} + \frac{1080982}{1147}e^{7} - \frac{22952527}{9176}e^{5} + \frac{5761003}{2294}e^{3} - \frac{1399157}{9176}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $-\frac{15}{62}e^{13} + \frac{1031}{124}e^{11} - \frac{6547}{62}e^{9} + \frac{37987}{62}e^{7} - \frac{101289}{62}e^{5} + \frac{205183}{124}e^{3} - \frac{6987}{62}e$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $-\frac{1603}{36704}e^{13} + \frac{375}{248}e^{11} - \frac{714689}{36704}e^{9} + \frac{532793}{4588}e^{7} - \frac{12048025}{36704}e^{5} + \frac{3528825}{9176}e^{3} - \frac{3258843}{36704}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $1$