# Properties

 Base field 3.3.733.1 Weight [2, 2, 2] Level norm 20 Level $[20, 20, w^{2} - 4]$ Label 3.3.733.1-20.2-b Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.733.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 7x + 8$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[20, 20, w^{2} - 4]$ Label 3.3.733.1-20.2-b Dimension 4 Is CM no Is base change no Parent newspace dimension 6

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut +\mathstrut 2x^{3}$$ $$\mathstrut -\mathstrut 12x^{2}$$ $$\mathstrut -\mathstrut 20x$$ $$\mathstrut +\mathstrut 17$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}0$
4 $[4, 2, -w^{2} - w + 5]$ $\phantom{-}e$
5 $[5, 5, -w + 3]$ $-1$
7 $[7, 7, -w^{2} - 2w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{9}{2}e + \frac{9}{2}$
11 $[11, 11, -w^{2} + 5]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{11}{2}e - \frac{3}{2}$
13 $[13, 13, w + 1]$ $\phantom{-}e^{2} - 5$
23 $[23, 23, w^{2} - 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{7}{2}$
25 $[25, 5, w^{2} + 2w - 1]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{9}{2}e + \frac{13}{2}$
27 $[27, 3, -3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{7}{2}e + \frac{3}{2}$
29 $[29, 29, -3w + 7]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{11}{2}e + \frac{15}{2}$
43 $[43, 43, -3w^{2} - 2w + 17]$ $\phantom{-}e^{3} - 11e - 2$
49 $[49, 7, -2w^{2} + w + 11]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + \frac{11}{2}e + \frac{17}{2}$
67 $[67, 67, -2w^{2} - 4w + 3]$ $-e^{3} + 9e + 4$
71 $[71, 71, -2w^{2} + w + 9]$ $\phantom{-}e^{2} + 2e - 5$
73 $[73, 73, w^{2} + 2w - 7]$ $\phantom{-}e^{3} - e^{2} - 7e + 9$
73 $[73, 73, -2w^{2} - 2w + 11]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{7}{2}e - \frac{17}{2}$
73 $[73, 73, w - 5]$ $\phantom{-}\frac{3}{2}e^{3} - \frac{1}{2}e^{2} - \frac{33}{2}e - \frac{1}{2}$
89 $[89, 89, 2w^{2} + w - 9]$ $-e^{3} - e^{2} + 7e + 7$
89 $[89, 89, -w^{2} - 2w + 9]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + \frac{13}{2}e + \frac{25}{2}$
89 $[89, 89, -2w - 1]$ $-e^{3} - 2e^{2} + 11e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $-1$
5 $[5, 5, -w + 3]$ $1$