Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 11 Level $[11, 11, -w^{2} + 2w + 2]$ Label 3.3.761.1-11.1-a Dimension 5 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 $[11, 11, -w^{2} + 2w + 2]$ Label 3.3.761.1-11.1-a Dimension 5 Is CM no Is base change no Parent newspace dimension 10

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 8x + 1$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}e^{4} - 2e^{3} - 7e^{2} + 9e + 6$
8 $[8, 2, 2]$ $-\frac{4}{3}e^{4} + \frac{10}{3}e^{3} + \frac{23}{3}e^{2} - 14e - \frac{14}{3}$
9 $[9, 3, -w^{2} + 2w + 4]$ $-e^{4} + 2e^{3} + 6e^{2} - 8e - 1$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}1$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}e^{4} - 2e^{3} - 6e^{2} + 7e + 4$
19 $[19, 19, w + 3]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{4}{3}e^{3} - \frac{5}{3}e^{2} + 5e + \frac{5}{3}$
19 $[19, 19, -w^{2} + 2w + 5]$ $-e^{2} + 2e + 3$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}\frac{4}{3}e^{4} - \frac{7}{3}e^{3} - \frac{26}{3}e^{2} + 8e + \frac{29}{3}$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}\frac{5}{3}e^{4} - \frac{11}{3}e^{3} - \frac{31}{3}e^{2} + 16e + \frac{25}{3}$
23 $[23, 23, -w^{2} + 2]$ $-2e^{4} + 4e^{3} + 13e^{2} - 18e - 6$
23 $[23, 23, -w + 4]$ $\phantom{-}\frac{1}{3}e^{4} - \frac{4}{3}e^{3} + \frac{1}{3}e^{2} + 6e - \frac{16}{3}$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}\frac{4}{3}e^{4} - \frac{13}{3}e^{3} - \frac{23}{3}e^{2} + 21e + \frac{20}{3}$
43 $[43, 43, w^{2} - 3w - 3]$ $-e^{4} + 3e^{3} + 4e^{2} - 14e$
49 $[49, 7, w^{2} - 6]$ $-\frac{7}{3}e^{4} + \frac{16}{3}e^{3} + \frac{41}{3}e^{2} - 19e - \frac{35}{3}$
53 $[53, 53, 2w - 5]$ $-\frac{10}{3}e^{4} + \frac{25}{3}e^{3} + \frac{59}{3}e^{2} - 38e - \frac{41}{3}$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-2e^{4} + 4e^{3} + 13e^{2} - 13e - 13$
71 $[71, 71, 2w - 3]$ $\phantom{-}\frac{4}{3}e^{4} - \frac{7}{3}e^{3} - \frac{32}{3}e^{2} + 11e + \frac{20}{3}$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}5e^{4} - 13e^{3} - 29e^{2} + 54e + 24$
83 $[83, 83, w^{2} - w - 9]$ $-\frac{1}{3}e^{4} - \frac{2}{3}e^{3} + \frac{8}{3}e^{2} + 5e - \frac{2}{3}$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

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