# Properties

 Base field 4.4.8069.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} - w + 1]$ Label 4.4.8069.1-19.2-c Dimension 5 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8069.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 5x^{2} + 5x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19, 19, -w^{2} - w + 1]$ Label 4.4.8069.1-19.2-c 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:
$$x^{5}$$ $$\mathstrut -\mathstrut 7x^{4}$$ $$\mathstrut +\mathstrut 5x^{3}$$ $$\mathstrut +\mathstrut 52x^{2}$$ $$\mathstrut -\mathstrut 101x$$ $$\mathstrut +\mathstrut 25$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $-\frac{2}{5}e^{4} + \frac{7}{5}e^{3} + \frac{17}{5}e^{2} - \frac{52}{5}e - 1$
7 $[7, 7, -w^{3} + 4w - 1]$ $-e^{4} + 4e^{3} + 7e^{2} - 32e + 10$
13 $[13, 13, -w^{2} + 3]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{26}{5}e^{3} - \frac{36}{5}e^{2} + \frac{201}{5}e - 15$
16 $[16, 2, 2]$ $\phantom{-}\frac{2}{5}e^{4} - \frac{7}{5}e^{3} - \frac{12}{5}e^{2} + \frac{52}{5}e - 10$
17 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{6}{5}e^{3} - \frac{6}{5}e^{2} + \frac{51}{5}e$
17 $[17, 17, -w^{3} + 5w - 2]$ $\phantom{-}\frac{3}{5}e^{4} - \frac{13}{5}e^{3} - \frac{18}{5}e^{2} + \frac{103}{5}e - 7$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{6}{5}e^{3} - \frac{1}{5}e^{2} + \frac{51}{5}e - 9$
19 $[19, 19, -w^{2} - w + 1]$ $-1$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $\phantom{-}\frac{1}{5}e^{4} - \frac{1}{5}e^{3} - \frac{11}{5}e^{2} + \frac{6}{5}e + 6$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{11}{5}e^{4} - \frac{41}{5}e^{3} - \frac{81}{5}e^{2} + \frac{311}{5}e - 8$
43 $[43, 43, w^{3} - w^{2} - 4w + 2]$ $\phantom{-}e^{3} - 2e^{2} - 8e + 8$
43 $[43, 43, w^{3} - 6w]$ $\phantom{-}\frac{7}{5}e^{4} - \frac{27}{5}e^{3} - \frac{52}{5}e^{2} + \frac{222}{5}e - 11$
47 $[47, 47, -w^{3} - w^{2} + 5w]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{26}{5}e^{3} - \frac{46}{5}e^{2} + \frac{206}{5}e$
49 $[49, 7, w^{2} + 2w - 2]$ $\phantom{-}\frac{6}{5}e^{4} - \frac{26}{5}e^{3} - \frac{36}{5}e^{2} + \frac{191}{5}e - 17$
59 $[59, 59, 2w^{3} - 8w + 3]$ $\phantom{-}\frac{14}{5}e^{4} - \frac{59}{5}e^{3} - \frac{89}{5}e^{2} + \frac{454}{5}e - 29$
67 $[67, 67, w^{2} - w - 4]$ $-2e^{4} + 8e^{3} + 13e^{2} - 65e + 29$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-2e^{4} + 8e^{3} + 15e^{2} - 64e + 8$
81 $[81, 3, -3]$ $-\frac{7}{5}e^{4} + \frac{32}{5}e^{3} + \frac{42}{5}e^{2} - \frac{252}{5}e + 14$
97 $[97, 97, w^{3} + w^{2} - 5w + 1]$ $-\frac{12}{5}e^{4} + \frac{47}{5}e^{3} + \frac{82}{5}e^{2} - \frac{372}{5}e + 19$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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