# Properties

 Base field 3.3.940.1 Weight [2, 2, 2] Level norm 4 Level $[4, 4, w]$ Label 3.3.940.1-4.3-a Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.940.1

Generator $$w$$, with minimal polynomial $$x^{3} - 7x - 4$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2] Level $[4, 4, w]$ Label 3.3.940.1-4.3-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:
$$x^{4} - 8x^{2} + 2x + 8$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}0$
2 $[2, 2, -w - 1]$ $\phantom{-}e$
5 $[5, 5, -w^{2} + w + 7]$ $-\frac{1}{2}e^{3} - e^{2} + 2e + 4$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}\frac{1}{2}e^{3} - 2e + 2$
17 $[17, 17, -w^{2} + 3w + 1]$ $\phantom{-}\frac{1}{2}e^{3} - 4e + 2$
23 $[23, 23, -w^{2} + w + 3]$ $-e^{3} + 8e$
27 $[27, 3, 3]$ $-2e^{2} - 2e + 8$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 4e$
37 $[37, 37, w^{2} + w + 1]$ $-\frac{3}{2}e^{3} - e^{2} + 10e$
41 $[41, 41, w^{2} - w - 9]$ $-\frac{3}{2}e^{3} - e^{2} + 8e + 4$
43 $[43, 43, -3w^{2} + 3w + 17]$ $\phantom{-}e^{3} + 2e^{2} - 8e - 8$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{3} - 2e^{2} + 6e + 4$
47 $[47, 47, -2w + 5]$ $\phantom{-}2e^{2} - 2e - 8$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}\frac{3}{2}e^{3} - 8e - 2$
59 $[59, 59, 2w - 1]$ $\phantom{-}e^{3} - 10e$
67 $[67, 67, w^{2} + w - 5]$ $\phantom{-}2e^{2} + 2e - 12$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{3} - 4e - 4$
79 $[79, 79, 3w^{2} - w - 23]$ $\phantom{-}e^{3} - 6e + 8$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-\frac{3}{2}e^{3} - 2e^{2} + 6e + 14$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-\frac{1}{2}e^{3} + e^{2} + 6e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$