# Properties

 Label 4.4.18097.1-9.1-b Base field 4.4.18097.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 9, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 4]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18097.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 6x + 4$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 9, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 4]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} - 2x - 1$$
Norm Prime Eigenvalue
3 $[3, 3, -w + 1]$ $\phantom{-}0$
4 $[4, 2, w]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{7}{2}w - 3]$ $-e + 2$
7 $[7, 7, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + \frac{5}{2}w - 2]$ $-2e$
13 $[13, 13, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{7}{2}w - 1]$ $\phantom{-}2e - 4$
17 $[17, 17, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w]$ $\phantom{-}0$
27 $[27, 3, -w^{3} + 7w + 1]$ $-2$
31 $[31, 31, w + 3]$ $\phantom{-}2e - 4$
31 $[31, 31, -w^{2} + 5]$ $-4e + 2$
37 $[37, 37, w^{2} - 3]$ $\phantom{-}4e - 6$
41 $[41, 41, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - \frac{3}{2}w - 2]$ $\phantom{-}6e - 6$
47 $[47, 47, w^{3} - 5w - 3]$ $\phantom{-}6$
53 $[53, 53, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w]$ $-6$
61 $[61, 61, w^{3} - w^{2} - 5w + 3]$ $\phantom{-}4e - 12$
83 $[83, 83, w^{3} + w^{2} - 6w - 7]$ $\phantom{-}6$
83 $[83, 83, -w^{3} + 5w + 1]$ $-6e + 12$
83 $[83, 83, 2w - 1]$ $-6$
83 $[83, 83, -\frac{3}{2}w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 2]$ $\phantom{-}0$
89 $[89, 89, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{7}{2}w - 2]$ $-12e + 12$
89 $[89, 89, w^{3} - 5w + 5]$ $\phantom{-}0$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w + 1]$ $-1$