# Properties

 Label 4.4.725.1-131.1-a Base field 4.4.725.1 Weight $[2, 2, 2, 2]$ Level norm $131$ Level $[131, 131, -3w^{3} + 2w^{2} + 8w - 2]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.725.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[131, 131, -3w^{3} + 2w^{2} + 8w - 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 4x - 8$$
Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $-e + 2$
16 $[16, 2, 2]$ $-\frac{1}{2}e + 1$
19 $[19, 19, -w^{3} + 2w + 2]$ $\phantom{-}\frac{1}{2}e + 3$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-e - 1$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{2}e - 3$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-e - 2$
31 $[31, 31, w^{3} - 4w + 1]$ $\phantom{-}e - 2$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}e - 2$
41 $[41, 41, 2w^{2} - w - 3]$ $-e - 1$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-\frac{3}{2}e + 5$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}e - 6$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}2e - 7$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $\phantom{-}7$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $-3e + 10$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $-2e - 6$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}2e + 1$
81 $[81, 3, -3]$ $\phantom{-}4e - 10$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-2e + 4$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $\phantom{-}2e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$131$ $[131, 131, -3w^{3} + 2w^{2} + 8w - 2]$ $1$