# Properties

 Label 4.4.19025.1-16.3-b Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16,4,w^{2} - 2w - 7]$ Dimension $14$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19025.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16,4,w^{2} - 2w - 7]$ Dimension: $14$ 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:

 $$x^{14} + 6x^{13} - 14x^{12} - 141x^{11} - 60x^{10} + 1043x^{9} + 1491x^{8} - 2425x^{7} - 5740x^{6} - 360x^{5} + 4765x^{4} + 1475x^{3} - 1045x^{2} - 150x + 25$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $\phantom{-}e$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}0$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $...$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $...$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $...$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $...$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $...$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $...$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $...$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $...$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $...$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $...$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $...$
81 $[81, 3, -3]$ $...$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $...$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $...$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,w^{2} - 7]$ $-1$