Properties

 Base field 4.4.11525.1 Weight [2, 2, 2, 2] Level norm 19 Level $[19,19,w - 1]$ Label 4.4.11525.1-19.4-a Dimension 2 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 $[19,19,w - 1]$ Label 4.4.11525.1-19.4-a Dimension 2 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:
$$x^{2}$$ $$\mathstrut +\mathstrut 2x$$ $$\mathstrut -\mathstrut 4$$
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 $[11, 11, w + 1]$ $-\frac{1}{2}e - 3$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{1}{2}e - 2$
16 $[16, 2, 2]$ $-\frac{1}{2}e - 3$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-\frac{5}{2}e - 5$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}3e + 3$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-\frac{1}{2}e + 2$
19 $[19, 19, w - 1]$ $\phantom{-}1$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{1}{2}e + 3$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}5$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-3e - 3$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}e + 6$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-4e + 1$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}2e - 3$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-7$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{5}{2}e + 3$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{5}{2}e - 7$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}5e + 8$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{9}{2}e + 2$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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