# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} + 3w + 2]$ Label 3.3.761.1-19.3-d Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.761.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 6x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[19, 19, -w^{2} + 3w + 2]$ Label 3.3.761.1-19.3-d Dimension 6 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6} + 3x^{5} - 18x^{4} - 20x^{3} + 113x^{2} - 87x + 9$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-\frac{17}{375}e^{5} - \frac{24}{125}e^{4} + \frac{13}{25}e^{3} + \frac{5}{3}e^{2} - \frac{796}{375}e - \frac{298}{125}$
7 $[7, 7, w - 1]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{89}{375}e^{5} - \frac{133}{125}e^{4} + \frac{71}{25}e^{3} + \frac{26}{3}e^{2} - \frac{6307}{375}e + \frac{359}{125}$
9 $[9, 3, -w^{2} + 2w + 4]$ $-\frac{14}{125}e^{5} - \frac{74}{125}e^{4} + \frac{13}{25}e^{3} + 4e^{2} - \frac{207}{125}e - \frac{398}{125}$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}\frac{4}{75}e^{5} + \frac{13}{25}e^{4} + \frac{4}{5}e^{3} - \frac{11}{3}e^{2} - \frac{448}{75}e + \frac{101}{25}$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{37}{125}e^{5} + \frac{142}{125}e^{4} - \frac{104}{25}e^{3} - 9e^{2} + \frac{2931}{125}e - \frac{966}{125}$
19 $[19, 19, w + 3]$ $-\frac{103}{375}e^{5} - \frac{116}{125}e^{4} + \frac{117}{25}e^{3} + \frac{25}{3}e^{2} - \frac{10139}{375}e + \frac{1018}{125}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{3}{25}e^{5} + \frac{23}{25}e^{4} + \frac{4}{5}e^{3} - 5e^{2} - \frac{111}{25}e + \frac{21}{25}$
19 $[19, 19, -w^{2} + 3w + 2]$ $-1$
23 $[23, 23, w^{2} - w - 3]$ $-\frac{9}{25}e^{5} - \frac{44}{25}e^{4} + \frac{13}{5}e^{3} + 11e^{2} - \frac{342}{25}e + \frac{112}{25}$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}\frac{16}{125}e^{5} + \frac{31}{125}e^{4} - \frac{72}{25}e^{3} - 3e^{2} + \frac{1683}{125}e - \frac{438}{125}$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{208}{375}e^{5} + \frac{301}{125}e^{4} - \frac{162}{25}e^{3} - \frac{55}{3}e^{2} + \frac{14129}{375}e - \frac{898}{125}$
31 $[31, 31, w^{2} - 5]$ $-\frac{32}{125}e^{5} - \frac{187}{125}e^{4} + \frac{19}{25}e^{3} + 10e^{2} - \frac{241}{125}e - \frac{499}{125}$
43 $[43, 43, w^{2} - 3w - 3]$ $-\frac{157}{375}e^{5} - \frac{229}{125}e^{4} + \frac{123}{25}e^{3} + \frac{40}{3}e^{2} - \frac{10991}{375}e + \frac{1417}{125}$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}\frac{436}{375}e^{5} + \frac{667}{125}e^{4} - \frac{304}{25}e^{3} - \frac{121}{3}e^{2} + \frac{25268}{375}e - \frac{1291}{125}$
53 $[53, 53, 2w - 5]$ $-\frac{7}{25}e^{5} - \frac{37}{25}e^{4} + \frac{9}{5}e^{3} + 9e^{2} - \frac{291}{25}e + \frac{226}{25}$
61 $[61, 61, 2w^{2} - 2w - 9]$ $\phantom{-}\frac{16}{75}e^{5} + \frac{27}{25}e^{4} - \frac{4}{5}e^{3} - \frac{14}{3}e^{2} + \frac{383}{75}e - \frac{271}{25}$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{116}{375}e^{5} + \frac{127}{125}e^{4} - \frac{149}{25}e^{3} - \frac{32}{3}e^{2} + \frac{13108}{375}e - \frac{1496}{125}$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}\frac{97}{125}e^{5} + \frac{477}{125}e^{4} - \frac{149}{25}e^{3} - 25e^{2} + \frac{3961}{125}e - \frac{921}{125}$
83 $[83, 83, w^{2} - w - 9]$ $\phantom{-}\frac{77}{125}e^{5} + \frac{282}{125}e^{4} - \frac{234}{25}e^{3} - 18e^{2} + \frac{6451}{125}e - \frac{2561}{125}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} + 3w + 2]$ $1$