# Properties

 Label 4.4.17600.1-4.1-b Base field 4.4.17600.1 Weight $[2, 2, 2, 2]$ Level norm $4$ Level $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ Dimension $1$ CM no Base change no

# Related objects

## Base field 4.4.17600.1

Generator $$w$$, with minimal polynomial $$x^{4} - 14x^{2} + 44$$; narrow class number $$2$$ and class number $$1$$.

## Form

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

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}1$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $\phantom{-}3$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}3$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $-6$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $-4$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $\phantom{-}5$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $-4$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $-4$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $-7$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $\phantom{-}3$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $-6$
31 $[31, 31, -w - 1]$ $-10$
31 $[31, 31, w - 1]$ $-1$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $-3$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $-12$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $\phantom{-}8$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $-1$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $\phantom{-}6$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $\phantom{-}6$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $-7$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $-1$