# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 41 Level $[41, 41, -2w^{2} + 3w + 6]$ Label 3.3.321.1-41.1-a Dimension 3 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 $[41, 41, -2w^{2} + 3w + 6]$ Label 3.3.321.1-41.1-a Dimension 3 Is CM no Is base change no Parent newspace dimension 11

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{3} + x^{2} - 5x + 1$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $\phantom{-}0$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}e^{2} + e - 5$
8 $[8, 2, 2]$ $-e^{2} - 2e + 2$
11 $[11, 11, -w^{2} + w + 1]$ $-e^{2} - 2e + 2$
23 $[23, 23, -w - 3]$ $-e^{2} + 7$
29 $[29, 29, -w^{2} + 2w + 4]$ $\phantom{-}3e^{2} + 6e - 9$
31 $[31, 31, 2w - 3]$ $-2e^{2} - 2e + 4$
41 $[41, 41, -2w^{2} + 3w + 6]$ $-1$
43 $[43, 43, w^{2} - 3w + 3]$ $-2e^{2} - 6e + 4$
47 $[47, 47, w^{2} + w - 4]$ $\phantom{-}4e^{2} + 6e - 13$
49 $[49, 7, 2w^{2} - 3w - 3]$ $\phantom{-}2e^{2} - 13$
53 $[53, 53, w^{2} - 3w - 2]$ $\phantom{-}e^{2} + 3e - 7$
59 $[59, 59, 2w^{2} - w - 5]$ $-2e^{2} - 7e + 4$
59 $[59, 59, w^{2} - w - 7]$ $\phantom{-}2e^{2} - 8$
59 $[59, 59, -w^{2} - w + 7]$ $\phantom{-}3e^{2} + 3e - 9$
67 $[67, 67, 2w^{2} - 3w - 7]$ $-2e^{2} - 2e + 1$
73 $[73, 73, -w^{2} + 4w - 5]$ $-e^{2} - 6e - 1$
79 $[79, 79, w^{2} - 8]$ $\phantom{-}2e^{2} + 6e$
79 $[79, 79, w^{2} - 5w + 5]$ $-3e^{2} - 4e + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
41 $[41, 41, -2w^{2} + 3w + 6]$ $1$