# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 21 Level $[21, 21, -w^{2} + 2w + 3]$ Label 3.3.321.1-21.1-b Dimension 2 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.321.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 4x + 1$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[21, 21, -w^{2} + 2w + 3]$ Label 3.3.321.1-21.1-b Dimension 2 Is CM no Is base change no Parent newspace dimension 3

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{2} - 8$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}1$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{2} - 2]$ $-1$
8 $[8, 2, 2]$ $-e + 1$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e$
23 $[23, 23, -w - 3]$ $-8$
29 $[29, 29, -w^{2} + 2w + 4]$ $-e + 2$
31 $[31, 31, 2w - 3]$ $-2e$
41 $[41, 41, -2w^{2} + 3w + 6]$ $-2e - 6$
43 $[43, 43, w^{2} - 3w + 3]$ $-e$
47 $[47, 47, w^{2} + w - 4]$ $-3e + 4$
49 $[49, 7, 2w^{2} - 3w - 3]$ $-4e + 2$
53 $[53, 53, w^{2} - 3w - 2]$ $-e - 6$
59 $[59, 59, 2w^{2} - w - 5]$ $\phantom{-}2e + 4$
59 $[59, 59, w^{2} - w - 7]$ $\phantom{-}2e + 4$
59 $[59, 59, -w^{2} - w + 7]$ $-2e + 4$
67 $[67, 67, 2w^{2} - 3w - 7]$ $\phantom{-}4e + 4$
73 $[73, 73, -w^{2} + 4w - 5]$ $\phantom{-}2e + 2$
79 $[79, 79, w^{2} - 8]$ $-2e + 8$
79 $[79, 79, w^{2} - 5w + 5]$ $\phantom{-}e + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
7 $[7, 7, w^{2} - 2]$ $1$