# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 19 Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-d Dimension 10 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1129.1

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

## Form

 Weight [2, 2, 2] Level $[19, 19, -w^{2} - w + 4]$ Label 3.3.1129.1-19.1-d Dimension 10 Is CM no Is base change no Parent newspace dimension 36

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{10}$$ $$\mathstrut -\mathstrut 24x^{8}$$ $$\mathstrut +\mathstrut 202x^{6}$$ $$\mathstrut -\mathstrut 704x^{4}$$ $$\mathstrut +\mathstrut 864x^{2}$$ $$\mathstrut -\mathstrut 128$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}\frac{1}{32}e^{8} - \frac{5}{8}e^{6} + \frac{61}{16}e^{4} - \frac{27}{4}e^{2}$
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{64}e^{9} - \frac{5}{16}e^{7} + \frac{61}{32}e^{5} - \frac{27}{8}e^{3} - e$
8 $[8, 2, 2]$ $-\frac{1}{8}e^{8} + \frac{9}{4}e^{6} - \frac{47}{4}e^{4} + \frac{33}{2}e^{2} + 2$
11 $[11, 11, -w^{2} + 5]$ $-\frac{1}{64}e^{9} + \frac{5}{16}e^{7} - \frac{69}{32}e^{5} + \frac{51}{8}e^{3} - \frac{13}{2}e$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{9}{4}e^{5} + \frac{45}{4}e^{3} - \frac{27}{2}e$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{16}e^{9} - \frac{9}{8}e^{7} + \frac{45}{8}e^{5} - \frac{21}{4}e^{3} - 9e$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}1$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-\frac{3}{32}e^{9} + \frac{15}{8}e^{7} - \frac{195}{16}e^{5} + \frac{121}{4}e^{3} - \frac{51}{2}e$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}\frac{1}{16}e^{7} - \frac{5}{4}e^{5} + \frac{61}{8}e^{3} - \frac{23}{2}e$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-\frac{3}{32}e^{9} + 2e^{7} - \frac{223}{16}e^{5} + \frac{71}{2}e^{3} - 23e$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}\frac{5}{64}e^{9} - \frac{23}{16}e^{7} + \frac{249}{32}e^{5} - \frac{85}{8}e^{3} - \frac{19}{2}e$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}\frac{1}{4}e^{6} - 4e^{4} + \frac{33}{2}e^{2} - 6$
61 $[61, 61, w^{2} + w - 10]$ $-2e^{2} + 6$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}\frac{1}{4}e^{7} - \frac{9}{2}e^{5} + \frac{45}{2}e^{3} - 28e$
73 $[73, 73, -w^{2} - 1]$ $-\frac{5}{16}e^{8} + \frac{23}{4}e^{6} - \frac{249}{8}e^{4} + \frac{101}{2}e^{2} - 18$
83 $[83, 83, w^{2} - w - 10]$ $-\frac{5}{16}e^{8} + 6e^{6} - \frac{281}{8}e^{4} + 66e^{2} - 14$
89 $[89, 89, -w^{2} + 4w - 2]$ $-\frac{3}{16}e^{8} + \frac{7}{2}e^{6} - \frac{155}{8}e^{4} + 32e^{2} - 7$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{8}e^{7} - \frac{3}{2}e^{5} + \frac{5}{4}e^{3} + 14e$
97 $[97, 97, -w^{2} - 4w - 5]$ $-\frac{3}{16}e^{8} + \frac{13}{4}e^{6} - \frac{127}{8}e^{4} + \frac{45}{2}e^{2} - 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19, 19, -w^{2} - w + 4]$ $-1$