# Properties

 Base field 3.3.940.1 Weight [2, 2, 2] Level norm 5 Level $[5, 5, -w^{2} + w + 5]$ Label 3.3.940.1-5.2-c 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 $[5, 5, -w^{2} + w + 5]$ Label 3.3.940.1-5.2-c Dimension 4 Is CM no Is base change no Parent newspace dimension 7

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4} - x^{3} - 6x^{2} + 7x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
2 $[2, 2, -w - 1]$ $\phantom{-}e^{3} - 5e + 2$
5 $[5, 5, -w^{2} + w + 7]$ $\phantom{-}e^{2} - 3$
5 $[5, 5, -w^{2} + w + 5]$ $\phantom{-}1$
17 $[17, 17, -w^{2} + 3w + 1]$ $-e^{2} + 5$
23 $[23, 23, -w^{2} + w + 3]$ $-2e^{3} + e^{2} + 10e - 5$
27 $[27, 3, 3]$ $\phantom{-}e^{3} - e^{2} - 7e + 9$
29 $[29, 29, -w^{2} + 3w - 1]$ $\phantom{-}e^{3} + 2e^{2} - 3e - 6$
37 $[37, 37, w^{2} + w + 1]$ $-e^{3} - e^{2} + 3e - 1$
41 $[41, 41, w^{2} - w - 9]$ $\phantom{-}e^{3} - 2e^{2} - 7e + 10$
43 $[43, 43, -3w^{2} + 3w + 17]$ $-2e^{3} + 12e - 4$
47 $[47, 47, 2w^{2} - 2w - 13]$ $-e^{2} + 13$
47 $[47, 47, -2w + 5]$ $\phantom{-}e^{3} + e^{2} - 5e + 5$
53 $[53, 53, 3w^{2} - w - 19]$ $\phantom{-}2e^{2} - 8$
59 $[59, 59, 2w - 1]$ $-e^{3} - e^{2} + 3e - 1$
67 $[67, 67, w^{2} + w - 5]$ $-4e^{3} - 4e^{2} + 16e + 10$
71 $[71, 71, -3w^{2} + w + 21]$ $\phantom{-}e^{2} - 3$
79 $[79, 79, 3w^{2} - w - 23]$ $-e^{3} + e^{2} + 3e + 1$
89 $[89, 89, 2w^{2} - 4w - 7]$ $-5e^{3} - 3e^{2} + 27e - 5$
89 $[89, 89, -2w^{2} - 2w + 5]$ $-e^{2} + 4e - 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w^{2} + w + 5]$ $-1$