# Properties

 Label 4.4.16317.1-9.1-c Base field 4.4.16317.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, w^{3} - w^{2} - 4w]$ Dimension $4$ 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: $[9, 3, w^{3} - w^{2} - 4w]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} - 16x^{2} + 4$$
Norm Prime Eigenvalue
5 $[5, 5, w + 1]$ $\phantom{-}e$
5 $[5, 5, -w + 2]$ $\phantom{-}\frac{1}{2}e^{3} - 8e$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}\frac{1}{2}e^{2} - 3$
7 $[7, 7, -w^{2} + 2]$ $-\frac{1}{2}e^{2} + 5$
9 $[9, 3, w^{3} - w^{2} - 4w]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}1$
17 $[17, 17, -w^{3} + 2w^{2} + 3w - 2]$ $-\frac{1}{2}e^{3} + 9e$
17 $[17, 17, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
25 $[25, 5, w^{2} - w - 3]$ $\phantom{-}4$
37 $[37, 37, 2w - 1]$ $\phantom{-}6$
43 $[43, 43, -w^{3} + 2w^{2} + 2w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - 3$
43 $[43, 43, w^{3} - w^{2} - 3w + 1]$ $-\frac{1}{2}e^{2} + 5$
59 $[59, 59, 2w - 5]$ $\phantom{-}\frac{1}{2}e^{3} - 11e$
59 $[59, 59, -2w - 3]$ $-\frac{3}{2}e^{3} + 25e$
79 $[79, 79, -w^{3} + 2w^{2} + 5w - 4]$ $\phantom{-}e^{2} - 6$
79 $[79, 79, -w^{3} + w^{2} + 6w - 2]$ $-e^{2} + 10$
83 $[83, 83, -w^{3} + 7w]$ $-\frac{3}{2}e^{3} + 23e$
83 $[83, 83, -w^{3} + 2w^{2} + 4w - 2]$ $-\frac{1}{2}e^{3} + 9e$
83 $[83, 83, -w^{3} + w^{2} + 5w - 3]$ $\phantom{-}\frac{1}{2}e^{3} - 9e$
83 $[83, 83, w^{2} - 2w - 6]$ $-\frac{1}{2}e^{3} + 5e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w^{3} - w^{2} - 4w]$ $1$