# Properties

 Label 4.4.16317.1-17.2-d Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17,17,w^{3} - w^{2} - 4w + 2]$ Dimension $13$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.16317.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17,17,w^{3} - w^{2} - 4w + 2]$ Dimension: $13$ 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:

 $$x^{13} + 3x^{12} - 29x^{11} - 77x^{10} + 298x^{9} + 629x^{8} - 1450x^{7} - 2151x^{6} + 3247x^{5} + 3482x^{4} - 3006x^{3} - 2511x^{2} + 756x + 441$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $...$
7 $[7, 7, -w^{2} + 2w + 1]$ $...$
7 $[7, 7, -w^{2} + 2]$ $...$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $...$
16 $[16, 2, 2]$ $...$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $...$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}1$
25 $[25, 5, w^{2} - w - 3]$ $...$
37 $[37, 37, 2w - 1]$ $...$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $...$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $...$
59 $[59, 59, 2w - 5]$ $...$
59 $[59, 59, -2w - 3]$ $...$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $...$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $...$
83 $[83, 83, -w^{3} + 7w]$ $...$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $...$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $...$
83 $[83, 83, w^{2} - 2w - 6]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17,17,w^{3} - w^{2} - 4w + 2]$ $-1$