# Properties

 Base field 4.4.15952.1 Weight [2, 2, 2, 2] Level norm 11 Level $[11, 11, -w^{3} + 5w + 1]$ Label 4.4.15952.1-11.1-a Dimension 11 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15952.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} - 2x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[11, 11, -w^{3} + 5w + 1]$ Label 4.4.15952.1-11.1-a Dimension 11 Is CM no Is base change no Parent newspace dimension 22

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{11}$$ $$\mathstrut -\mathstrut 5x^{10}$$ $$\mathstrut -\mathstrut 4x^{9}$$ $$\mathstrut +\mathstrut 48x^{8}$$ $$\mathstrut -\mathstrut 19x^{7}$$ $$\mathstrut -\mathstrut 152x^{6}$$ $$\mathstrut +\mathstrut 90x^{5}$$ $$\mathstrut +\mathstrut 203x^{4}$$ $$\mathstrut -\mathstrut 100x^{3}$$ $$\mathstrut -\mathstrut 107x^{2}$$ $$\mathstrut +\mathstrut 27x$$ $$\mathstrut +\mathstrut 9$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -w^{3} + w^{2} + 5w - 2]$ $\phantom{-}\frac{2}{9}e^{10} - \frac{8}{9}e^{9} - \frac{13}{9}e^{8} + \frac{71}{9}e^{7} + 2e^{6} - \frac{193}{9}e^{5} - \frac{22}{9}e^{4} + 22e^{3} + \frac{55}{9}e^{2} - \frac{20}{3}e - 2$
11 $[11, 11, -w^{3} + 5w + 1]$ $-1$
11 $[11, 11, -w + 2]$ $-\frac{5}{9}e^{10} + \frac{23}{9}e^{9} + \frac{16}{9}e^{8} - \frac{188}{9}e^{7} + \frac{37}{3}e^{6} + \frac{424}{9}e^{5} - \frac{401}{9}e^{4} - \frac{98}{3}e^{3} + \frac{317}{9}e^{2} + \frac{16}{3}e - 3$
13 $[13, 13, -w^{3} + w^{2} + 4w + 1]$ $\phantom{-}\frac{2}{9}e^{10} + \frac{1}{9}e^{9} - \frac{40}{9}e^{8} - \frac{1}{9}e^{7} + 26e^{6} - \frac{22}{9}e^{5} - \frac{472}{9}e^{4} + 2e^{3} + \frac{289}{9}e^{2} + \frac{10}{3}e$
17 $[17, 17, -w^{3} + w^{2} + 6w - 1]$ $-\frac{1}{3}e^{10} + e^{9} + 4e^{8} - \frac{35}{3}e^{7} - \frac{52}{3}e^{6} + \frac{134}{3}e^{5} + \frac{100}{3}e^{4} - \frac{181}{3}e^{3} - \frac{77}{3}e^{2} + \frac{58}{3}e + 4$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{2}{9}e^{10} - \frac{1}{9}e^{9} + \frac{49}{9}e^{8} - \frac{26}{9}e^{7} - 34e^{6} + \frac{238}{9}e^{5} + \frac{643}{9}e^{4} - 53e^{3} - \frac{442}{9}e^{2} + \frac{77}{3}e + 3$
23 $[23, 23, w^{3} - 6w]$ $\phantom{-}e^{10} - \frac{14}{3}e^{9} - \frac{10}{3}e^{8} + \frac{118}{3}e^{7} - \frac{65}{3}e^{6} - 96e^{5} + \frac{244}{3}e^{4} + \frac{247}{3}e^{3} - 66e^{2} - \frac{67}{3}e + 7$
27 $[27, 3, w^{3} + w^{2} - 5w - 4]$ $-\frac{8}{9}e^{10} + \frac{26}{9}e^{9} + \frac{58}{9}e^{8} - \frac{209}{9}e^{7} - \frac{32}{3}e^{6} + \frac{430}{9}e^{5} + \frac{19}{9}e^{4} - \frac{56}{3}e^{3} - \frac{40}{9}e^{2} - \frac{23}{3}e + 8$
41 $[41, 41, -w^{3} + w^{2} + 5w]$ $\phantom{-}e^{10} - \frac{13}{3}e^{9} - \frac{14}{3}e^{8} + \frac{110}{3}e^{7} - \frac{25}{3}e^{6} - 91e^{5} + \frac{125}{3}e^{4} + \frac{248}{3}e^{3} - 33e^{2} - \frac{80}{3}e + 6$
41 $[41, 41, 2w^{3} - 11w - 4]$ $-\frac{13}{9}e^{10} + \frac{52}{9}e^{9} + \frac{71}{9}e^{8} - \frac{439}{9}e^{7} + 4e^{6} + \frac{1079}{9}e^{5} - \frac{433}{9}e^{4} - 107e^{3} + \frac{385}{9}e^{2} + \frac{100}{3}e - 2$
53 $[53, 53, 2w^{3} - 2w^{2} - 11w + 6]$ $-\frac{7}{9}e^{10} + \frac{10}{9}e^{9} + \frac{104}{9}e^{8} - \frac{127}{9}e^{7} - 57e^{6} + \frac{536}{9}e^{5} + \frac{923}{9}e^{4} - 98e^{3} - \frac{467}{9}e^{2} + \frac{154}{3}e - 1$
59 $[59, 59, 2w^{3} - 11w - 2]$ $\phantom{-}\frac{1}{9}e^{10} - \frac{4}{9}e^{9} - \frac{11}{9}e^{8} + \frac{49}{9}e^{7} + 5e^{6} - \frac{200}{9}e^{5} - \frac{83}{9}e^{4} + 29e^{3} + \frac{32}{9}e^{2} + \frac{2}{3}e + 5$
67 $[67, 67, w^{3} - 7w - 1]$ $-\frac{1}{9}e^{10} + \frac{13}{9}e^{9} - \frac{25}{9}e^{8} - \frac{112}{9}e^{7} + 33e^{6} + \frac{290}{9}e^{5} - \frac{916}{9}e^{4} - 32e^{3} + \frac{913}{9}e^{2} + \frac{37}{3}e - 16$
71 $[71, 71, 3w^{3} - 2w^{2} - 15w + 1]$ $\phantom{-}\frac{2}{3}e^{10} - 3e^{9} - 3e^{8} + \frac{82}{3}e^{7} - \frac{31}{3}e^{6} - \frac{229}{3}e^{5} + \frac{166}{3}e^{4} + \frac{227}{3}e^{3} - \frac{170}{3}e^{2} - \frac{59}{3}e + 12$
79 $[79, 79, -3w^{3} + w^{2} + 16w + 3]$ $-\frac{1}{9}e^{10} + \frac{7}{9}e^{9} - \frac{1}{9}e^{8} - \frac{64}{9}e^{7} + \frac{16}{3}e^{6} + \frac{191}{9}e^{5} - \frac{85}{9}e^{4} - \frac{80}{3}e^{3} - \frac{23}{9}e^{2} + 10e + 4$
89 $[89, 89, -4w^{3} + 2w^{2} + 22w - 3]$ $\phantom{-}\frac{1}{9}e^{10} - \frac{16}{9}e^{9} + \frac{46}{9}e^{8} + \frac{82}{9}e^{7} - \frac{136}{3}e^{6} + \frac{70}{9}e^{5} + \frac{868}{9}e^{4} - \frac{163}{3}e^{3} - \frac{454}{9}e^{2} + 36e - 7$
101 $[101, 101, -2w^{3} + 13w + 6]$ $\phantom{-}\frac{1}{9}e^{10} + \frac{26}{9}e^{9} - \frac{131}{9}e^{8} - \frac{119}{9}e^{7} + \frac{352}{3}e^{6} - \frac{227}{9}e^{5} - \frac{2501}{9}e^{4} + \frac{337}{3}e^{3} + \frac{1832}{9}e^{2} - \frac{182}{3}e - 13$
101 $[101, 101, w^{3} + w^{2} - 6w - 3]$ $-\frac{11}{9}e^{10} + \frac{65}{9}e^{9} - \frac{26}{9}e^{8} - \frac{473}{9}e^{7} + \frac{247}{3}e^{6} + \frac{733}{9}e^{5} - \frac{2000}{9}e^{4} + \frac{64}{3}e^{3} + \frac{1484}{9}e^{2} - \frac{164}{3}e - 16$
101 $[101, 101, -3w^{3} + 2w^{2} + 17w - 3]$ $-\frac{19}{9}e^{10} + \frac{82}{9}e^{9} + \frac{104}{9}e^{8} - \frac{736}{9}e^{7} + \frac{17}{3}e^{6} + \frac{2000}{9}e^{5} - \frac{595}{9}e^{4} - \frac{625}{3}e^{3} + \frac{445}{9}e^{2} + \frac{128}{3}e - 4$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 5w + 1]$ $1$