# Properties

 Base field 4.4.725.1 Weight [2, 2, 2, 2] Level norm 139 Level $[139,139,w^{3} + 2w^{2} - 4w - 4]$ Label 4.4.725.1-139.3-a Dimension 1 CM no Base change no

# Related objects

## 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 $[139,139,w^{3} + 2w^{2} - 4w - 4]$ Label 4.4.725.1-139.3-a Dimension 1 Is CM no Is base change no Parent newspace dimension 2

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}2$
11 $[11, 11, w^{3} - 3w]$ $\phantom{-}6$
16 $[16, 2, 2]$ $\phantom{-}1$
19 $[19, 19, -w^{3} + 2w + 2]$ $-3$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-2$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}2$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $-1$
31 $[31, 31, w^{3} - 4w + 1]$ $-9$
31 $[31, 31, -w^{2} + 2w + 3]$ $-9$
41 $[41, 41, 2w^{2} - w - 3]$ $\phantom{-}4$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-4$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $-1$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}4$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $-13$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $\phantom{-}2$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}13$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $-16$
81 $[81, 3, -3]$ $-14$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-10$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $\phantom{-}3$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
139 $[139,139,w^{3} + 2w^{2} - 4w - 4]$ $1$