# Properties

 Label 4.4.17069.1-16.1-g Base field 4.4.17069.1 Weight $[2, 2, 2, 2]$ Level norm $16$ Level $[16, 2, 2]$ Dimension $13$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.17069.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} - 4x + 3$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[16, 2, 2]$ Dimension: $13$ CM: no Base change: yes Newspace dimension: $36$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{13} + 3x^{12} - 23x^{11} - 68x^{10} + 187x^{9} + 554x^{8} - 631x^{7} - 1957x^{6} + 796x^{5} + 2828x^{4} - 244x^{3} - 1052x^{2} + 324x - 20$$
Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w^{3} - 2w^{2} - 6w + 1]$ $\phantom{-}e$
9 $[9, 3, w^{3} - 2w^{2} - 5w + 1]$ $...$
16 $[16, 2, 2]$ $-1$
17 $[17, 17, w^{3} - w^{2} - 8w - 5]$ $...$
17 $[17, 17, -2w^{3} + 4w^{2} + 11w - 2]$ $...$
17 $[17, 17, -w^{3} + 3w^{2} + 2w - 2]$ $...$
17 $[17, 17, w^{3} - 2w^{2} - 4w + 1]$ $...$
25 $[25, 5, w^{3} - 3w^{2} - 3w + 1]$ $...$
25 $[25, 5, w^{2} - 2w - 7]$ $...$
29 $[29, 29, w^{3} - 2w^{2} - 6w - 1]$ $...$
29 $[29, 29, w - 2]$ $...$
53 $[53, 53, w^{3} - 3w^{2} - 4w + 4]$ $...$
53 $[53, 53, -w^{3} + 3w^{2} + 4w - 5]$ $...$
61 $[61, 61, -w^{3} + 2w^{2} + 7w - 4]$ $...$
61 $[61, 61, -4w^{3} + 11w^{2} + 14w - 8]$ $...$
101 $[101, 101, -w^{3} + 2w^{2} + 7w - 1]$ $...$
103 $[103, 103, -w^{3} + 3w^{2} + 2w - 5]$ $...$
103 $[103, 103, -w^{3} + w^{2} + 8w + 2]$ $...$
113 $[113, 113, w^{3} - 3w^{2} - 3w + 7]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$16$ $[16, 2, 2]$ $1$