# Properties

 Label 4.4.725.1-109.1-b Base field 4.4.725.1 Weight $[2, 2, 2, 2]$ Level norm $109$ Level $[109, 109, 3w^{3} - 5w^{2} - 5w + 3]$ 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: $[109, 109, 3w^{3} - 5w^{2} - 5w + 3]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $2$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}1$
11 $[11, 11, w^{3} - 3w]$ $-3$
16 $[16, 2, 2]$ $\phantom{-}7$
19 $[19, 19, -w^{3} + 2w + 2]$ $-2$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $\phantom{-}6$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $-4$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}0$
31 $[31, 31, w^{3} - 4w + 1]$ $-6$
31 $[31, 31, -w^{2} + 2w + 3]$ $-1$
41 $[41, 41, 2w^{2} - w - 3]$ $\phantom{-}6$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-10$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $-1$
49 $[49, 7, w^{2} + w - 3]$ $-10$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $-3$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $\phantom{-}12$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}16$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $-1$
81 $[81, 3, -3]$ $\phantom{-}5$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-14$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $-7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$109$ $[109, 109, 3w^{3} - 5w^{2} - 5w + 3]$ $1$