# Properties

 Label 4.4.8112.1-13.2-a Base field 4.4.8112.1 Weight $[2, 2, 2, 2]$ Level norm $13$ Level $[13,13,-w^{3} + 4w + 2]$ Dimension $1$ CM no Base change no

# Learn more about

## Base field 4.4.8112.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[13,13,-w^{3} + 4w + 2]$ Dimension: $1$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}3$
4 $[4, 2, w^{2} - w - 1]$ $\phantom{-}1$
9 $[9, 3, -w^{2} + 2]$ $-1$
13 $[13, 13, w^{3} - 4w + 2]$ $-2$
13 $[13, 13, -w^{3} + 4w + 2]$ $-1$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}7$
17 $[17, 17, -w^{3} + 3w - 1]$ $-1$
29 $[29, 29, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}4$
29 $[29, 29, w^{3} - w^{2} - 4w + 2]$ $-8$
43 $[43, 43, w^{2} + w - 4]$ $\phantom{-}1$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}9$
53 $[53, 53, w^{3} - 2w - 2]$ $\phantom{-}8$
53 $[53, 53, -w^{3} + 2w - 2]$ $-12$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}16$
79 $[79, 79, -w^{3} - w^{2} + 4w + 1]$ $\phantom{-}12$
101 $[101, 101, -w^{3} + w^{2} + 3w - 5]$ $-18$
101 $[101, 101, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}6$
103 $[103, 103, 2w^{2} - w - 4]$ $-8$
103 $[103, 103, 2w^{2} + w - 4]$ $\phantom{-}12$
107 $[107, 107, 2w^{2} + w - 5]$ $\phantom{-}8$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,-w^{3} + 4w + 2]$ $1$