# Properties

 Label 4.4.16317.1-5.1-a Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $5$ Level $[5, 5, w + 1]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16317.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 4x^{2} + 5x + 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[5, 5, w + 1]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 2x - 2$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $-1$
5 $[5, 5, -w + 2]$ $\phantom{-}e$
7 $[7, 7, -w^{2} + 2w + 1]$ $-e - 1$
7 $[7, 7, -w^{2} + 2]$ $\phantom{-}e - 2$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-e + 2$
16 $[16, 2, 2]$ $\phantom{-}e - 5$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $-e + 1$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $-3e + 1$
25 $[25, 5, w^{2} - w - 3]$ $-2$
37 $[37, 37, 2w - 1]$ $\phantom{-}e - 1$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $-e - 2$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-3e + 10$
59 $[59, 59, 2w - 5]$ $\phantom{-}10$
59 $[59, 59, -2w - 3]$ $\phantom{-}2e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}7e - 2$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $\phantom{-}e + 1$
83 $[83, 83, -w^{3} + 7w]$ $\phantom{-}4e - 3$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $\phantom{-}10$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $-3e + 8$
83 $[83, 83, w^{2} - 2w - 6]$ $-5e + 9$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w + 1]$ $1$