# Properties

 Label 4.4.6809.1-31.1-b Base field 4.4.6809.1 Weight $[2, 2, 2, 2]$ Level norm $31$ Level $[31, 31, -w^{3} + 6w + 2]$ Dimension $14$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.6809.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[31, 31, -w^{3} + 6w + 2]$ Dimension: $14$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{14} - 5x^{13} - 10x^{12} + 80x^{11} - 477x^{9} + 305x^{8} + 1313x^{7} - 1265x^{6} - 1603x^{5} + 1976x^{4} + 558x^{3} - 1101x^{2} + 143x + 83$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} - 4w]$ $...$
8 $[8, 2, w^{3} - w^{2} - 4w + 3]$ $...$
11 $[11, 11, w^{3} - 5w + 1]$ $...$
17 $[17, 17, -w^{3} - w^{2} + 5w + 4]$ $...$
23 $[23, 23, -w^{2} + 2]$ $...$
29 $[29, 29, -w^{2} - w + 3]$ $...$
31 $[31, 31, -w^{3} + 6w + 2]$ $-1$
43 $[43, 43, w^{3} - 6w]$ $...$
47 $[47, 47, 2w^{3} - 9w]$ $...$
47 $[47, 47, -2w^{3} + w^{2} + 8w - 2]$ $...$
53 $[53, 53, -4w^{3} + 2w^{2} + 18w - 5]$ $...$
59 $[59, 59, w^{2} - w - 5]$ $...$
59 $[59, 59, 3w^{3} - 15w - 5]$ $...$
71 $[71, 71, w^{3} - 3w - 3]$ $...$
81 $[81, 3, -3]$ $...$
83 $[83, 83, -2w^{3} + 8w + 3]$ $...$
89 $[89, 89, -2w^{3} + 11w - 2]$ $...$
101 $[101, 101, 2w^{3} - w^{2} - 10w]$ $...$
101 $[101, 101, 2w^{3} - 2w^{2} - 10w + 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$31$ $[31, 31, -w^{3} + 6w + 2]$ $1$