# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} + 2w + 5]$ Label 3.3.761.1-19.2-a Dimension 8 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.761.1

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

## Form

 Weight [2, 2, 2] Level $[19, 19, -w^{2} + 2w + 5]$ Label 3.3.761.1-19.2-a Dimension 8 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:
$$x^{8} - 2x^{7} - 16x^{6} + 32x^{5} + 72x^{4} - 156x^{3} - 64x^{2} + 240x - 104$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-e^{7} + \frac{3}{4}e^{6} + 17e^{5} - 11e^{4} - 86e^{3} + 51e^{2} + 126e - 88$
8 $[8, 2, 2]$ $-\frac{3}{2}e^{7} + e^{6} + \frac{51}{2}e^{5} - \frac{29}{2}e^{4} - \frac{259}{2}e^{3} + 68e^{2} + 191e - 125$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}\frac{3}{4}e^{7} - \frac{1}{2}e^{6} - \frac{25}{2}e^{5} + 7e^{4} + \frac{123}{2}e^{3} - 31e^{2} - 87e + 56$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{1}{4}e^{6} - 4e^{5} + 3e^{4} + \frac{37}{2}e^{3} - 9e^{2} - 23e + 10$
13 $[13, 13, -w^{2} + w + 4]$ $-\frac{1}{2}e^{7} + \frac{1}{2}e^{6} + \frac{17}{2}e^{5} - \frac{15}{2}e^{4} - 44e^{3} + 35e^{2} + 69e - 56$
19 $[19, 19, w + 3]$ $\phantom{-}\frac{7}{2}e^{7} - \frac{5}{2}e^{6} - 59e^{5} + \frac{71}{2}e^{4} + 295e^{3} - 159e^{2} - 422e + 276$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}1$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{1}{2}e^{6} - 8e^{5} + 7e^{4} + \frac{73}{2}e^{3} - 28e^{2} - 45e + 38$
23 $[23, 23, w^{2} - w - 3]$ $-\frac{11}{4}e^{7} + 2e^{6} + \frac{93}{2}e^{5} - \frac{57}{2}e^{4} - \frac{467}{2}e^{3} + 128e^{2} + 336e - 220$
23 $[23, 23, -w^{2} + 2]$ $-\frac{1}{2}e^{7} + \frac{1}{4}e^{6} + 8e^{5} - 3e^{4} - \frac{73}{2}e^{3} + 11e^{2} + 44e - 18$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{7}{4}e^{7} - \frac{5}{4}e^{6} - \frac{59}{2}e^{5} + \frac{35}{2}e^{4} + 147e^{3} - 77e^{2} - 207e + 132$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}\frac{9}{4}e^{7} - \frac{7}{4}e^{6} - \frac{75}{2}e^{5} + 25e^{4} + 185e^{3} - 110e^{2} - 263e + 178$
43 $[43, 43, w^{2} - 3w - 3]$ $\phantom{-}e^{7} - e^{6} - \frac{33}{2}e^{5} + 14e^{4} + \frac{161}{2}e^{3} - 58e^{2} - 113e + 86$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}\frac{1}{4}e^{7} - 5e^{5} + \frac{1}{2}e^{4} + 31e^{3} - 7e^{2} - 58e + 26$
53 $[53, 53, 2w - 5]$ $\phantom{-}\frac{7}{4}e^{7} - \frac{5}{4}e^{6} - \frac{59}{2}e^{5} + 18e^{4} + 148e^{3} - 84e^{2} - 217e + 152$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-e^{7} + \frac{3}{4}e^{6} + \frac{33}{2}e^{5} - 10e^{4} - \frac{161}{2}e^{3} + 41e^{2} + 113e - 68$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{15}{4}e^{7} - 3e^{6} - 63e^{5} + \frac{87}{2}e^{4} + 314e^{3} - 195e^{2} - 452e + 318$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}\frac{1}{2}e^{7} - 9e^{5} - \frac{1}{2}e^{4} + \frac{97}{2}e^{3} + e^{2} - 74e + 22$
83 $[83, 83, w^{2} - w - 9]$ $\phantom{-}\frac{5}{4}e^{7} - \frac{3}{4}e^{6} - 21e^{5} + 11e^{4} + 104e^{3} - 53e^{2} - 145e + 96$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} + 2w + 5]$ $-1$