# Properties

 Label 4.4.17609.1-5.1-a Base field 4.4.17609.1 Weight $[2, 2, 2, 2]$ Level norm $5$ Level $[5, 5, w^{3} + w^{2} - 4w + 1]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[5, 5, w^{3} + w^{2} - 4w + 1]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{6} - 10x^{4} + 21x^{2} - 4$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-1$
7 $[7, 7, -w^{3} + 6w - 2]$ $\phantom{-}\frac{1}{2}e^{5} - \frac{9}{2}e^{3} + 8e$
8 $[8, 2, w^{3} - 7w + 3]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + \frac{21}{2}e$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 9$
17 $[17, 17, -w^{2} - w + 3]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 6e$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-e^{5} + \frac{19}{2}e^{3} - \frac{33}{2}e$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $-\frac{3}{2}e^{5} + 14e^{3} - \frac{45}{2}e$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e^{3} - 5e$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $\phantom{-}\frac{3}{2}e^{4} - \frac{27}{2}e^{2} + 14$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $\phantom{-}\frac{1}{2}e^{5} - 6e^{3} + \frac{39}{2}e$
59 $[59, 59, -2w^{3} + 13w - 6]$ $-e^{5} + 10e^{3} - 23e$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $-\frac{3}{2}e^{4} + \frac{17}{2}e^{2} + 3$
59 $[59, 59, w^{2} + w - 1]$ $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} + \frac{1}{2}e$
59 $[59, 59, w^{2} + 2w - 6]$ $-2e^{2} + 8$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $\phantom{-}e^{5} - 8e^{3} + 7e$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $\phantom{-}0$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-2e^{5} + 16e^{3} - 18e$
81 $[81, 3, -3]$ $-2e^{2} + 8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w^{3} + w^{2} - 4w + 1]$ $1$