# Properties

 Label 4.4.18432.1-9.1-b Base field 4.4.18432.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, w - 3]$ Dimension $1$ CM no Base change yes

# Related objects

## Base field 4.4.18432.1

Generator $$w$$, with minimal polynomial $$x^{4} - 12x^{2} + 18$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, w - 3]$ Dimension: $1$ CM: no Base change: yes Newspace dimension: $18$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $-2$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-2$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-2$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-2$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $-2$
9 $[9, 3, w - 3]$ $-1$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}2$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}2$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}2$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}2$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $-12$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-12$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-12$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $-12$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-10$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-10$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-10$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-10$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $-2$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-2$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, w - 3]$ $1$