# Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19,19,-\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ Label 4.4.11525.1-19.3-a Dimension 6 CM no Base change no

# Related objects

• L-function not available

## 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 $[19,19,-\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ Label 4.4.11525.1-19.3-a Dimension 6 Is CM no Is base change no Parent newspace dimension 16

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut +\mathstrut 7x^{5}$$ $$\mathstrut +\mathstrut 6x^{4}$$ $$\mathstrut -\mathstrut 42x^{3}$$ $$\mathstrut -\mathstrut 75x^{2}$$ $$\mathstrut -\mathstrut 13x$$ $$\mathstrut +\mathstrut 15$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-\frac{5}{19}e^{5} - \frac{12}{19}e^{4} + \frac{48}{19}e^{3} + \frac{69}{19}e^{2} - \frac{83}{19}e - \frac{51}{19}$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $-\frac{9}{19}e^{5} - \frac{14}{19}e^{4} + \frac{94}{19}e^{3} + \frac{52}{19}e^{2} - \frac{119}{19}e - \frac{12}{19}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{26}{19}e^{5} + \frac{89}{19}e^{4} - \frac{147}{19}e^{3} - \frac{507}{19}e^{2} - \frac{222}{19}e + \frac{60}{19}$
16 $[16, 2, 2]$ $\phantom{-}e^{5} + 3e^{4} - 7e^{3} - 17e^{2} - e + 2$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-\frac{31}{19}e^{5} - \frac{120}{19}e^{4} + \frac{157}{19}e^{3} + \frac{747}{19}e^{2} + \frac{272}{19}e - \frac{244}{19}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{10}{19}e^{5} - \frac{24}{19}e^{4} + \frac{77}{19}e^{3} + \frac{100}{19}e^{2} - \frac{33}{19}e - \frac{7}{19}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}1$
19 $[19, 19, w - 1]$ $-\frac{20}{19}e^{5} - \frac{67}{19}e^{4} + \frac{116}{19}e^{3} + \frac{371}{19}e^{2} + \frac{143}{19}e + \frac{5}{19}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{8}{19}e^{5} + \frac{4}{19}e^{4} - \frac{92}{19}e^{3} + \frac{53}{19}e^{2} + \frac{148}{19}e - \frac{78}{19}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $-\frac{31}{19}e^{5} - \frac{120}{19}e^{4} + \frac{138}{19}e^{3} + \frac{709}{19}e^{2} + \frac{424}{19}e - \frac{168}{19}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $\phantom{-}\frac{22}{19}e^{5} + \frac{68}{19}e^{4} - \frac{158}{19}e^{3} - \frac{391}{19}e^{2} + \frac{65}{19}e + \frac{137}{19}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{16}{19}e^{5} + \frac{46}{19}e^{4} - \frac{127}{19}e^{3} - \frac{274}{19}e^{2} + \frac{125}{19}e + \frac{167}{19}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-\frac{24}{19}e^{5} - \frac{107}{19}e^{4} + \frac{67}{19}e^{3} + \frac{658}{19}e^{2} + \frac{487}{19}e - \frac{241}{19}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}\frac{18}{19}e^{5} + \frac{66}{19}e^{4} - \frac{93}{19}e^{3} - \frac{389}{19}e^{2} - \frac{180}{19}e - \frac{52}{19}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-\frac{14}{19}e^{5} - \frac{45}{19}e^{4} + \frac{85}{19}e^{3} + \frac{235}{19}e^{2} + \frac{7}{19}e - \frac{25}{19}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{61}{19}e^{5} - \frac{211}{19}e^{4} + \frac{350}{19}e^{3} + \frac{1237}{19}e^{2} + \frac{458}{19}e - \frac{322}{19}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{41}{19}e^{5} + \frac{125}{19}e^{4} - \frac{291}{19}e^{3} - \frac{733}{19}e^{2} - \frac{30}{19}e + \frac{270}{19}$
71 $[71, 71, w^{2} - 8]$ $-\frac{9}{19}e^{5} - \frac{14}{19}e^{4} + \frac{113}{19}e^{3} + \frac{71}{19}e^{2} - \frac{290}{19}e - \frac{126}{19}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{31}{19}e^{5} + \frac{158}{19}e^{4} - \frac{43}{19}e^{3} - \frac{994}{19}e^{2} - \frac{842}{19}e + \frac{92}{19}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-1$