# Properties

 Base field 3.3.733.1 Weight [2, 2, 2] Level norm 16 Level $[16, 4, w^{2} - w - 3]$ Label 3.3.733.1-16.2-c Dimension 8 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 $[16, 4, w^{2} - w - 3]$ Label 3.3.733.1-16.2-c Dimension 8 Is CM no Is base change no Parent newspace dimension 13

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{8}$$ $$\mathstrut +\mathstrut x^{7}$$ $$\mathstrut -\mathstrut 13x^{6}$$ $$\mathstrut -\mathstrut 9x^{5}$$ $$\mathstrut +\mathstrut 50x^{4}$$ $$\mathstrut +\mathstrut 17x^{3}$$ $$\mathstrut -\mathstrut 47x^{2}$$ $$\mathstrut +\mathstrut 3x$$ $$\mathstrut +\mathstrut 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 5]$ $\phantom{-}0$
5 $[5, 5, -w + 3]$ $\phantom{-}\frac{1}{2}e^{7} - \frac{11}{2}e^{5} + 16e^{3} + \frac{3}{2}e^{2} - 9e + \frac{1}{2}$
7 $[7, 7, -w^{2} - 2w + 3]$ $\phantom{-}e^{6} - e^{5} - 9e^{4} + 9e^{3} + 16e^{2} - 12e$
11 $[11, 11, -w^{2} + 5]$ $-e^{5} + 8e^{3} - e^{2} - 11e + 1$
13 $[13, 13, w + 1]$ $\phantom{-}\frac{1}{2}e^{7} + e^{6} - \frac{13}{2}e^{5} - 10e^{4} + 25e^{3} + \frac{47}{2}e^{2} - 21e - \frac{5}{2}$
23 $[23, 23, w^{2} - 3]$ $\phantom{-}2e^{6} - 3e^{5} - 19e^{4} + 25e^{3} + 37e^{2} - 30e - 4$
25 $[25, 5, w^{2} + 2w - 1]$ $-\frac{1}{2}e^{7} - e^{6} + \frac{15}{2}e^{5} + 9e^{4} - 34e^{3} - \frac{33}{2}e^{2} + 37e + \frac{5}{2}$
27 $[27, 3, -3]$ $-e^{6} + e^{5} + 9e^{4} - 9e^{3} - 17e^{2} + 12e + 5$
29 $[29, 29, -3w + 7]$ $\phantom{-}\frac{3}{2}e^{7} - \frac{35}{2}e^{5} + 58e^{3} + \frac{5}{2}e^{2} - 50e + \frac{7}{2}$
43 $[43, 43, -3w^{2} - 2w + 17]$ $-e^{7} + 11e^{5} + e^{4} - 31e^{3} - 8e^{2} + 15e + 1$
49 $[49, 7, -2w^{2} + w + 11]$ $\phantom{-}e^{7} - 12e^{5} + 40e^{3} + e^{2} - 31e + 3$
67 $[67, 67, -2w^{2} - 4w + 3]$ $-2e^{5} + e^{4} + 16e^{3} - 10e^{2} - 20e + 11$
71 $[71, 71, -2w^{2} + w + 9]$ $-e^{7} - 3e^{6} + 16e^{5} + 26e^{4} - 75e^{3} - 42e^{2} + 72e - 1$
73 $[73, 73, w^{2} + 2w - 7]$ $-\frac{1}{2}e^{7} + e^{6} + \frac{5}{2}e^{5} - 7e^{4} + 8e^{3} - \frac{5}{2}e^{2} - 18e + \frac{17}{2}$
73 $[73, 73, -2w^{2} - 2w + 11]$ $-\frac{1}{2}e^{7} + \frac{13}{2}e^{5} - e^{4} - 25e^{3} + \frac{15}{2}e^{2} + 21e - \frac{13}{2}$
73 $[73, 73, w - 5]$ $\phantom{-}e^{7} - 2e^{6} - 8e^{5} + 17e^{4} + 6e^{3} - 22e^{2} + 15e + 3$
89 $[89, 89, 2w^{2} + w - 9]$ $-\frac{5}{2}e^{7} - e^{6} + \frac{61}{2}e^{5} + 11e^{4} - 105e^{3} - \frac{63}{2}e^{2} + 81e - \frac{1}{2}$
89 $[89, 89, -w^{2} - 2w + 9]$ $\phantom{-}2e^{7} + 2e^{6} - 24e^{5} - 19e^{4} + 81e^{3} + 42e^{2} - 59e + 1$
89 $[89, 89, -2w - 1]$ $\phantom{-}\frac{1}{2}e^{7} + e^{6} - \frac{9}{2}e^{5} - 9e^{4} + 8e^{3} + \frac{41}{2}e^{2} + 4e - \frac{5}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

The Atkin-Lehner eigenvalues for this form are not in the database.