# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 27 Level $[27, 3, 3]$ Label 3.3.761.1-27.1-g Dimension 4 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 $[27, 3, 3]$ Label 3.3.761.1-27.1-g Dimension 4 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} + 3x^{3} - 26x^{2} - 44x + 184$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
7 $[7, 7, w - 1]$ $\phantom{-}e$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - 4e + 2$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}1$
11 $[11, 11, -w^{2} + 2w + 2]$ $\phantom{-}e^{2} + e - 14$
13 $[13, 13, -w^{2} + w + 4]$ $-e^{2} - 2e + 16$
19 $[19, 19, w + 3]$ $\phantom{-}e^{2} + e - 12$
19 $[19, 19, -w^{2} + 2w + 5]$ $-e - 2$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}e + 2$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}e^{2} + e - 16$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e^{2} + e - 16$
23 $[23, 23, -w + 4]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e - 2$
31 $[31, 31, w^{2} - 5]$ $-e^{2} - 2e + 12$
43 $[43, 43, w^{2} - 3w - 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - 7e + 8$
53 $[53, 53, 2w - 5]$ $\phantom{-}4$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 7e + 14$
71 $[71, 71, 2w - 3]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 8e + 6$
73 $[73, 73, 2w^{2} - 5w - 5]$ $-e^{2} + 10$
83 $[83, 83, w^{2} - w - 9]$ $-2e^{2} - 4e + 24$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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