# Properties

 Label 4.4.8069.1-19.2-d Base field 4.4.8069.1 Weight $[2, 2, 2, 2]$ Level norm $19$ Level $[19, 19, -w^{2} - w + 1]$ 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: $[19, 19, -w^{2} - w + 1]$ Dimension: $5$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{5} + 7x^{4} + 5x^{3} - 52x^{2} - 101x - 25$$
Norm Prime Eigenvalue
5 $[5, 5, w^{3} - 4w]$ $\phantom{-}e$
7 $[7, 7, w + 1]$ $\phantom{-}\frac{2}{5}e^{4} + \frac{7}{5}e^{3} - \frac{17}{5}e^{2} - \frac{52}{5}e + 1$
7 $[7, 7, -w^{3} + 4w - 1]$ $\phantom{-}e^{4} + 4e^{3} - 7e^{2} - 32e - 10$
13 $[13, 13, -w^{2} + 3]$ $-\frac{6}{5}e^{4} - \frac{26}{5}e^{3} + \frac{36}{5}e^{2} + \frac{201}{5}e + 15$
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 $[17, 17, w^{3} + w^{2} - 4w - 2]$ $-\frac{1}{5}e^{4} - \frac{6}{5}e^{3} + \frac{6}{5}e^{2} + \frac{51}{5}e$
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 $[19, 19, -w^{2} - w + 1]$ $\phantom{-}1$
29 $[29, 29, 2w^{3} - w^{2} - 9w + 5]$ $-\frac{1}{5}e^{4} - \frac{1}{5}e^{3} + \frac{11}{5}e^{2} + \frac{6}{5}e - 6$
41 $[41, 41, -w^{3} + w^{2} + 5w - 3]$ $-\frac{11}{5}e^{4} - \frac{41}{5}e^{3} + \frac{81}{5}e^{2} + \frac{311}{5}e + 8$
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 $[59, 59, 2w^{3} - 8w + 3]$ $-\frac{14}{5}e^{4} - \frac{59}{5}e^{3} + \frac{89}{5}e^{2} + \frac{454}{5}e + 29$
67 $[67, 67, w^{2} - w - 4]$ $\phantom{-}2e^{4} + 8e^{3} - 13e^{2} - 65e - 29$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}2e^{4} + 8e^{3} - 15e^{2} - 64e - 8$
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
$19$ $[19, 19, -w^{2} - w + 1]$ $-1$