# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 9 Level $[9, 3, -w^{2} + 2w + 4]$ Label 3.3.761.1-9.1-a Dimension 3 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 $[9, 3, -w^{2} + 2w + 4]$ Label 3.3.761.1-9.1-a Dimension 3 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:
$$x^{3} - 2x^{2} - 4x + 4$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{1}{2}e^{2}$
8 $[8, 2, 2]$ $-e^{2} + e + 1$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}e^{2} - e$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{2}e^{2} - e$
19 $[19, 19, w + 3]$ $-\frac{1}{2}e^{2} + 2e$
19 $[19, 19, -w^{2} + 2w + 5]$ $-e^{2} + 6$
19 $[19, 19, -w^{2} + 3w + 2]$ $-2e^{2} + e + 8$
23 $[23, 23, w^{2} - w - 3]$ $-\frac{1}{2}e^{2} + 3e$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}\frac{1}{2}e^{2} - 3e - 2$
23 $[23, 23, -w + 4]$ $-e - 2$
31 $[31, 31, w^{2} - 5]$ $-2e$
43 $[43, 43, w^{2} - 3w - 3]$ $-\frac{5}{2}e^{2} + e + 10$
49 $[49, 7, w^{2} - 6]$ $-\frac{1}{2}e^{2} - 4e + 4$
53 $[53, 53, 2w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - 4$
61 $[61, 61, 2w^{2} - 2w - 9]$ $\phantom{-}e^{2} + 6$
71 $[71, 71, 2w - 3]$ $-2e^{2} + 4$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}e^{2} - e + 2$
83 $[83, 83, w^{2} - w - 9]$ $-e^{2} + 2e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2w + 4]$ $-1$