# Properties

 Base field 3.3.761.1 Weight [2, 2, 2] Level norm 7 Level $[7, 7, w - 1]$ Label 3.3.761.1-7.1-a 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 $[7, 7, w - 1]$ Label 3.3.761.1-7.1-a Dimension 4 Is CM no Is base change no Parent newspace dimension 4

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 10x^{2} + 4$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $\phantom{-}1$
8 $[8, 2, 2]$ $-e^{2} + 5$
9 $[9, 3, -w^{2} + 2w + 4]$ $\phantom{-}0$
11 $[11, 11, -w^{2} + 2w + 2]$ $-e^{3} + 9e$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}e$
19 $[19, 19, w + 3]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}0$
19 $[19, 19, -w^{2} + 3w + 2]$ $\phantom{-}e^{3} - 11e$
23 $[23, 23, w^{2} - w - 3]$ $\phantom{-}e^{3} - 10e$
23 $[23, 23, -w^{2} + 2]$ $\phantom{-}e$
23 $[23, 23, -w + 4]$ $\phantom{-}4$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}e^{2} - 4$
43 $[43, 43, w^{2} - 3w - 3]$ $-e^{3} + 12e$
49 $[49, 7, w^{2} - 6]$ $-e^{2} + 6$
53 $[53, 53, 2w - 5]$ $\phantom{-}e^{2} - 2$
61 $[61, 61, 2w^{2} - 2w - 9]$ $-2e$
71 $[71, 71, 2w - 3]$ $-8$
73 $[73, 73, 2w^{2} - 5w - 5]$ $\phantom{-}2e^{3} - 16e$
83 $[83, 83, w^{2} - w - 9]$ $-2e^{2} + 16$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
7 $[7, 7, w - 1]$ $-1$