# Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ Label 4.4.11525.1-19.2-b Dimension 4 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 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ Label 4.4.11525.1-19.2-b Dimension 4 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:
$$x^{4}$$ $$\mathstrut -\mathstrut 6x^{2}$$ $$\mathstrut +\mathstrut 3x$$ $$\mathstrut +\mathstrut 3$$
Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-1$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}e$
11 $[11, 11, w + 1]$ $\phantom{-}e^{3} + 2e^{2} - 4e - 5$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $-e^{3} + 5e - 1$
16 $[16, 2, 2]$ $-e^{3} - 3e^{2} + 4e + 6$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}2e^{3} + e^{2} - 9e + 2$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}1$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-e^{3} + 3e - 3$
19 $[19, 19, w - 1]$ $-e^{3} - e^{2} + 3e - 2$
29 $[29, 29, w^{2} - w - 8]$ $-3e - 3$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $-e^{3} - e^{2} + 6e + 1$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-3e^{3} - 5e^{2} + 11e + 8$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}2e^{3} + 3e^{2} - 5e - 6$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-e^{3} - 3e^{2} + 3e + 10$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}3e^{3} + 3e^{2} - 18e - 3$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}4e^{3} + 3e^{2} - 16e - 2$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}4e^{3} + 2e^{2} - 19e + 1$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}e^{3} + e^{2} - 2$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}2e^{3} + 2e^{2} - 9e + 4$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-5e^{3} - 6e^{2} + 18e + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-1$