# Properties

 Base field 4.4.8789.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, w^{2} - w - 2]$ Label 4.4.8789.1-19.1-d Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8789.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 6x^{2} - 2x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, w^{2} - w - 2]$ Label 4.4.8789.1-19.1-d Dimension 5 Is CM no Is base change no Parent newspace dimension 12

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - x^{4} - 27x^{3} + 36x^{2} + 170x - 289$$
Norm Prime Eigenvalue
5 $[5, 5, -w^{3} + 2w^{2} + 3w]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-\frac{14}{17}e^{4} - \frac{20}{17}e^{3} + \frac{344}{17}e^{2} + \frac{295}{17}e - 110$
11 $[11, 11, -w^{3} + 2w^{2} + 4w]$ $\phantom{-}\frac{1}{17}e^{4} - \frac{1}{17}e^{3} - \frac{10}{17}e^{2} + \frac{19}{17}e - 2$
13 $[13, 13, -2w^{3} + 3w^{2} + 10w - 2]$ $-\frac{1}{17}e^{4} + \frac{1}{17}e^{3} + \frac{27}{17}e^{2} - \frac{19}{17}e - 10$
16 $[16, 2, 2]$ $-\frac{23}{17}e^{4} - \frac{28}{17}e^{3} + \frac{553}{17}e^{2} + \frac{413}{17}e - 168$
17 $[17, 17, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}\frac{22}{17}e^{4} + \frac{29}{17}e^{3} - \frac{526}{17}e^{2} - \frac{432}{17}e + 163$
17 $[17, 17, -w^{3} + w^{2} + 5w]$ $-\frac{8}{17}e^{4} - \frac{9}{17}e^{3} + \frac{182}{17}e^{2} + \frac{137}{17}e - 54$
17 $[17, 17, -w^{2} + 2w + 1]$ $\phantom{-}\frac{9}{17}e^{4} + \frac{8}{17}e^{3} - \frac{209}{17}e^{2} - \frac{101}{17}e + 63$
19 $[19, 19, w^{2} - w - 2]$ $-1$
29 $[29, 29, w^{3} - 2w^{2} - 5w]$ $-\frac{12}{17}e^{4} - \frac{22}{17}e^{3} + \frac{290}{17}e^{2} + \frac{316}{17}e - 90$
29 $[29, 29, w^{2} - w - 3]$ $\phantom{-}\frac{15}{17}e^{4} + \frac{19}{17}e^{3} - \frac{371}{17}e^{2} - \frac{310}{17}e + 121$
31 $[31, 31, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{15}{17}e^{4} - \frac{19}{17}e^{3} + \frac{354}{17}e^{2} + \frac{276}{17}e - 108$
43 $[43, 43, 2w^{3} - 3w^{2} - 11w]$ $\phantom{-}\frac{6}{17}e^{4} + \frac{11}{17}e^{3} - \frac{162}{17}e^{2} - \frac{175}{17}e + 60$
47 $[47, 47, w^{3} - 7w - 4]$ $-\frac{33}{17}e^{4} - \frac{35}{17}e^{3} + \frac{772}{17}e^{2} + \frac{512}{17}e - 226$
53 $[53, 53, -2w^{3} + 3w^{2} + 9w - 1]$ $-\frac{9}{17}e^{4} - \frac{8}{17}e^{3} + \frac{209}{17}e^{2} + \frac{101}{17}e - 61$
61 $[61, 61, -w - 3]$ $\phantom{-}\frac{10}{17}e^{4} + \frac{7}{17}e^{3} - \frac{253}{17}e^{2} - \frac{82}{17}e + 77$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $-\frac{2}{17}e^{4} + \frac{2}{17}e^{3} + \frac{54}{17}e^{2} - \frac{4}{17}e - 22$
73 $[73, 73, w^{3} - w^{2} - 7w - 1]$ $\phantom{-}\frac{22}{17}e^{4} + \frac{29}{17}e^{3} - \frac{543}{17}e^{2} - \frac{449}{17}e + 169$
81 $[81, 3, -3]$ $\phantom{-}e^{4} + e^{3} - 22e^{2} - 14e + 98$
83 $[83, 83, -2w^{3} + 3w^{2} + 9w + 1]$ $\phantom{-}\frac{8}{17}e^{4} + \frac{9}{17}e^{3} - \frac{199}{17}e^{2} - \frac{154}{17}e + 73$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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