# Properties

 Label 4.4.17600.1-16.1-e Base field 4.4.17600.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## 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: $[16, 2, 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $28$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 40x^{2} + 80$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{2}w^{3} + w^{2} + 4w - 8]$ $\phantom{-}0$
11 $[11, 11, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 4w + 11]$ $-2$
11 $[11, 11, -\frac{1}{2}w^{2} - w + 2]$ $\phantom{-}e$
11 $[11, 11, -\frac{1}{2}w^{2} + w + 2]$ $-e$
19 $[19, 19, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - 4w + 5]$ $-\frac{1}{8}e^{3} + \frac{9}{2}e$
19 $[19, 19, \frac{1}{2}w^{3} + w^{2} - 4w - 9]$ $-\frac{1}{4}e^{2} + 5$
19 $[19, 19, \frac{1}{2}w^{3} - w^{2} - 4w + 9]$ $-\frac{1}{4}e^{2} + 5$
19 $[19, 19, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 5]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{9}{2}e$
25 $[25, 5, \frac{1}{2}w^{2} - 1]$ $\phantom{-}\frac{1}{4}e^{2} - 9$
29 $[29, 29, \frac{1}{2}w^{3} - 4w - 1]$ $-\frac{1}{8}e^{3} + \frac{7}{2}e$
29 $[29, 29, -\frac{1}{2}w^{3} + 4w - 1]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{7}{2}e$
31 $[31, 31, -w - 1]$ $-\frac{1}{8}e^{3} + \frac{11}{2}e$
31 $[31, 31, w - 1]$ $\phantom{-}\frac{1}{8}e^{3} - \frac{11}{2}e$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 4w - 2]$ $\phantom{-}\frac{3}{16}e^{3} - \frac{29}{4}e$
41 $[41, 41, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 2]$ $-\frac{3}{16}e^{3} + \frac{29}{4}e$
49 $[49, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 7]$ $-\frac{1}{16}e^{3} + \frac{15}{4}e$
49 $[49, 7, \frac{3}{2}w^{3} - \frac{7}{2}w^{2} - 13w + 29]$ $\phantom{-}\frac{1}{16}e^{3} - \frac{15}{4}e$
59 $[59, 59, -\frac{1}{2}w^{3} - \frac{3}{2}w^{2} + 3w + 10]$ $-\frac{1}{4}e^{2} + 5$
59 $[59, 59, \frac{1}{2}w^{3} - \frac{3}{2}w^{2} - 3w + 10]$ $-\frac{1}{4}e^{2} + 5$
61 $[61, 61, \frac{1}{2}w^{2} + w - 6]$ $\phantom{-}\frac{1}{8}e^{2} - \frac{19}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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