# Properties

 Base field 4.4.17725.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, w + 1]$ Label 4.4.17725.1-19.1-e Dimension 6 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17725.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 12x^{2} + 13x + 41$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, w + 1]$ Label 4.4.17725.1-19.1-e Dimension 6 Is CM no Is base change no Parent newspace dimension 32

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut -\mathstrut 15x^{5}$$ $$\mathstrut +\mathstrut 79x^{4}$$ $$\mathstrut -\mathstrut 151x^{3}$$ $$\mathstrut -\mathstrut 46x^{2}$$ $$\mathstrut +\mathstrut 453x$$ $$\mathstrut -\mathstrut 364$$
Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}\frac{9}{29}e^{5} - \frac{98}{29}e^{4} + \frac{321}{29}e^{3} - \frac{136}{29}e^{2} - 30e + \frac{858}{29}$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $-\frac{14}{29}e^{5} + \frac{175}{29}e^{4} - \frac{683}{29}e^{3} + \frac{537}{29}e^{2} + 60e - \frac{2369}{29}$
19 $[19, 19, w + 1]$ $-1$
19 $[19, 19, -w^{2} + 6]$ $-\frac{19}{29}e^{5} + \frac{223}{29}e^{4} - \frac{813}{29}e^{3} + \frac{561}{29}e^{2} + 70e - \frac{2691}{29}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}5$
19 $[19, 19, -w + 2]$ $-\frac{11}{29}e^{5} + \frac{123}{29}e^{4} - \frac{402}{29}e^{3} + \frac{134}{29}e^{2} + 36e - \frac{923}{29}$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}\frac{1}{29}e^{5} - \frac{27}{29}e^{4} + \frac{171}{29}e^{3} - \frac{260}{29}e^{2} - 12e + \frac{685}{29}$
29 $[29, 29, -w^{2} + 9]$ $-\frac{25}{29}e^{5} + \frac{298}{29}e^{4} - \frac{1085}{29}e^{3} + \frac{671}{29}e^{2} + 96e - \frac{3292}{29}$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}\frac{24}{29}e^{5} - \frac{300}{29}e^{4} + \frac{1175}{29}e^{3} - \frac{933}{29}e^{2} - 104e + \frac{4144}{29}$
29 $[29, 29, w^{2} - 7]$ $-\frac{2}{29}e^{5} + \frac{25}{29}e^{4} - \frac{81}{29}e^{3} - \frac{2}{29}e^{2} + 7e + \frac{22}{29}$
29 $[29, 29, -w^{2} + 2w + 8]$ $\phantom{-}\frac{20}{29}e^{5} - \frac{221}{29}e^{4} + \frac{723}{29}e^{3} - \frac{299}{29}e^{2} - 63e + \frac{1955}{29}$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}\frac{9}{29}e^{5} - \frac{98}{29}e^{4} + \frac{350}{29}e^{3} - \frac{310}{29}e^{2} - 27e + \frac{1235}{29}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $\phantom{-}\frac{11}{29}e^{5} - \frac{181}{29}e^{4} + \frac{895}{29}e^{3} - \frac{1033}{29}e^{2} - 78e + \frac{3678}{29}$
41 $[41, 41, -w]$ $-\frac{2}{29}e^{5} + \frac{54}{29}e^{4} - \frac{342}{29}e^{3} + \frac{491}{29}e^{2} + 33e - \frac{1631}{29}$
41 $[41, 41, -w + 1]$ $-\frac{20}{29}e^{5} + \frac{250}{29}e^{4} - \frac{955}{29}e^{3} + \frac{647}{29}e^{2} + 86e - \frac{2970}{29}$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}\frac{17}{29}e^{5} - \frac{169}{29}e^{4} + \frac{500}{29}e^{3} - \frac{186}{29}e^{2} - 46e + \frac{1698}{29}$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-\frac{27}{29}e^{5} + \frac{265}{29}e^{4} - \frac{673}{29}e^{3} - \frac{230}{29}e^{2} + 64e - \frac{834}{29}$
61 $[61, 61, 2w^{2} - 3w - 14]$ $\phantom{-}e^{4} - 8e^{3} + 13e^{2} + 19e - 42$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{4}{29}e^{5} + \frac{50}{29}e^{4} - \frac{191}{29}e^{3} + \frac{112}{29}e^{2} + 18e - \frac{246}{29}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, w + 1]$ $1$