# Properties

 Base field 3.3.321.1 Weight [2, 2, 2] Level norm 43 Level $[43, 43, w^{2} - 3w + 3]$ Label 3.3.321.1-43.1-d Dimension 4 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 $[43, 43, w^{2} - 3w + 3]$ Label 3.3.321.1-43.1-d Dimension 4 Is CM no Is base change no Parent newspace dimension 10

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - 8x^{2} - 4x + 7$$
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{3}{2}$
3 $[3, 3, w - 1]$ $\phantom{-}e$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 4$
8 $[8, 2, 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{5}{2}e - \frac{7}{2}$
11 $[11, 11, -w^{2} + w + 1]$ $-e^{3} + 2e^{2} + 4e - 6$
23 $[23, 23, -w - 3]$ $\phantom{-}e^{3} - e^{2} - 6e + 2$
29 $[29, 29, -w^{2} + 2w + 4]$ $-\frac{3}{2}e^{3} + \frac{5}{2}e^{2} + \frac{17}{2}e - \frac{17}{2}$
31 $[31, 31, 2w - 3]$ $-3e + 1$
41 $[41, 41, -2w^{2} + 3w + 6]$ $-e^{3} + 2e^{2} + 4e - 7$
43 $[43, 43, w^{2} - 3w + 3]$ $-1$
47 $[47, 47, w^{2} + w - 4]$ $\phantom{-}2e^{2} - 3e - 7$
49 $[49, 7, 2w^{2} - 3w - 3]$ $\phantom{-}2e^{3} - 3e^{2} - 10e + 10$
53 $[53, 53, w^{2} - 3w - 2]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{7}{2}e^{2} - \frac{31}{2}e + \frac{7}{2}$
59 $[59, 59, 2w^{2} - w - 5]$ $\phantom{-}4e^{3} - 6e^{2} - 21e + 9$
59 $[59, 59, w^{2} - w - 7]$ $-\frac{3}{2}e^{3} + \frac{3}{2}e^{2} + \frac{19}{2}e - \frac{1}{2}$
59 $[59, 59, -w^{2} - w + 7]$ $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + \frac{9}{2}e + \frac{23}{2}$
67 $[67, 67, 2w^{2} - 3w - 7]$ $-2e^{2} + 2e + 8$
73 $[73, 73, -w^{2} + 4w - 5]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{3}{2}e^{2} - \frac{27}{2}e - \frac{9}{2}$
79 $[79, 79, w^{2} - 8]$ $-e^{3} - 2e^{2} + 9e + 8$
79 $[79, 79, w^{2} - 5w + 5]$ $-e^{3} + e^{2} + 4e + 2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
43 $[43, 43, w^{2} - 3w + 3]$ $1$