# Properties

 Base field 3.3.1129.1 Weight [2, 2, 2] Level norm 11 Level $[11, 11, -w^{2} + 5]$ Label 3.3.1129.1-11.1-d Dimension 6 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 $[11, 11, -w^{2} + 5]$ Label 3.3.1129.1-11.1-d Dimension 6 Is CM no Is base change no Parent newspace dimension 20

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{6}$$ $$\mathstrut +\mathstrut 3x^{5}$$ $$\mathstrut -\mathstrut 9x^{4}$$ $$\mathstrut -\mathstrut 28x^{3}$$ $$\mathstrut +\mathstrut 15x^{2}$$ $$\mathstrut +\mathstrut 63x$$ $$\mathstrut +\mathstrut 26$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{1}{3}e^{3} - \frac{7}{3}e^{2} - \frac{4}{3}e + \frac{1}{3}$
3 $[3, 3, w + 2]$ $-\frac{1}{3}e^{5} - \frac{2}{3}e^{4} + 3e^{3} + \frac{14}{3}e^{2} - 6e - \frac{19}{3}$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{1}{3}e^{2} - \frac{19}{3}e - \frac{23}{3}$
11 $[11, 11, -w^{2} + 5]$ $-1$
13 $[13, 13, w^{2} - w - 7]$ $-\frac{1}{3}e^{5} - e^{4} + \frac{5}{3}e^{3} + 6e^{2} - \frac{2}{3}e - \frac{20}{3}$
17 $[17, 17, -w^{2} + w + 4]$ $\phantom{-}\frac{2}{3}e^{4} + \frac{5}{3}e^{3} - \frac{11}{3}e^{2} - \frac{26}{3}e - \frac{1}{3}$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{4}{3}e^{4} - \frac{7}{3}e^{3} - \frac{28}{3}e^{2} + \frac{10}{3}e + 11$
29 $[29, 29, 2w^{2} - 2w - 11]$ $\phantom{-}\frac{1}{3}e^{5} + e^{4} - \frac{5}{3}e^{3} - 6e^{2} - \frac{1}{3}e + \frac{5}{3}$
31 $[31, 31, w^{2} - 2w - 4]$ $-e^{2} + 4$
37 $[37, 37, -2w^{2} + 3w + 7]$ $-\frac{1}{3}e^{5} - \frac{2}{3}e^{4} + 4e^{3} + \frac{17}{3}e^{2} - 12e - \frac{34}{3}$
41 $[41, 41, w^{2} - 2]$ $-e^{4} - 2e^{3} + 5e^{2} + 8e$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 3e^{3} - \frac{17}{3}e^{2} + 6e + \frac{40}{3}$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}e^{5} + \frac{5}{3}e^{4} - \frac{31}{3}e^{3} - \frac{41}{3}e^{2} + \frac{82}{3}e + \frac{86}{3}$
67 $[67, 67, 2w^{2} - w - 11]$ $\phantom{-}\frac{1}{3}e^{5} + e^{4} - \frac{2}{3}e^{3} - 4e^{2} - \frac{22}{3}e + \frac{2}{3}$
73 $[73, 73, -w^{2} - 1]$ $-e^{5} - \frac{7}{3}e^{4} + \frac{23}{3}e^{3} + \frac{37}{3}e^{2} - \frac{41}{3}e - \frac{19}{3}$
83 $[83, 83, w^{2} - w - 10]$ $-\frac{2}{3}e^{5} - 2e^{4} + \frac{16}{3}e^{3} + 12e^{2} - \frac{31}{3}e - \frac{25}{3}$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}e^{5} + \frac{1}{3}e^{4} - \frac{38}{3}e^{3} - \frac{13}{3}e^{2} + \frac{110}{3}e + \frac{52}{3}$
97 $[97, 97, w^{2} - 2w - 7]$ $\phantom{-}\frac{5}{3}e^{4} + \frac{11}{3}e^{3} - \frac{29}{3}e^{2} - \frac{50}{3}e - \frac{4}{3}$
97 $[97, 97, -w^{2} - 4w - 5]$ $-e^{5} - \frac{4}{3}e^{4} + \frac{35}{3}e^{3} + \frac{31}{3}e^{2} - \frac{110}{3}e - \frac{76}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{2} + 5]$ $1$