# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 49 Level $[49, 7, 2w^{2} - 3w - 3]$ Label 3.3.321.1-49.1-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 $[49, 7, 2w^{2} - 3w - 3]$ Label 3.3.321.1-49.1-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 $[3, 3, w + 1]$ $\phantom{-}0$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{2} - 2]$ $-e^{2} - e + 4$
8 $[8, 2, 2]$ $-e - 2$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}e^{2} - 5$
23 $[23, 23, -w - 3]$ $-\frac{3}{2}e^{2} - 2e + \frac{1}{2}$
29 $[29, 29, -w^{2} + 2w + 4]$ $\phantom{-}\frac{3}{2}e^{2} + 2e - \frac{5}{2}$
31 $[31, 31, 2w - 3]$ $\phantom{-}\frac{3}{2}e^{2} + 5e - \frac{11}{2}$
41 $[41, 41, -2w^{2} + 3w + 6]$ $-2e^{2} - e + 6$
43 $[43, 43, w^{2} - 3w + 3]$ $\phantom{-}3e^{2} + 4e - 9$
47 $[47, 47, w^{2} + w - 4]$ $\phantom{-}e^{2} - 8$
49 $[49, 7, 2w^{2} - 3w - 3]$ $-1$
53 $[53, 53, w^{2} - 3w - 2]$ $-\frac{1}{2}e^{2} - 5e - \frac{3}{2}$
59 $[59, 59, 2w^{2} - w - 5]$ $\phantom{-}2e - 4$
59 $[59, 59, w^{2} - w - 7]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{21}{2}$
59 $[59, 59, -w^{2} - w + 7]$ $\phantom{-}e^{2} - e - 10$
67 $[67, 67, 2w^{2} - 3w - 7]$ $-3e^{2} - 5e + 15$
73 $[73, 73, -w^{2} + 4w - 5]$ $-\frac{7}{2}e^{2} - 3e + \frac{11}{2}$
79 $[79, 79, w^{2} - 8]$ $\phantom{-}\frac{1}{2}e^{2} - 4e - \frac{11}{2}$
79 $[79, 79, w^{2} - 5w + 5]$ $-5e^{2} - 6e + 15$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
49 $[49, 7, 2w^{2} - 3w - 3]$ $1$