# Properties

 Label 4.4.18432.1-7.1-d Base field 4.4.18432.1 Weight $[2, 2, 2, 2]$ Level norm $7$ Level $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ Dimension $2$ CM no Base change no

# Related objects

• L-function not available

## 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: $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{2} + x - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}1$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-3e - 2$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}e - 1$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}2e - 1$
9 $[9, 3, w - 3]$ $\phantom{-}2e + 1$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}e + 7$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}4e + 9$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-5e + 2$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}2e - 7$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $-7e - 7$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}6e + 1$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $-6e - 2$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $-2e - 1$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}2e - 8$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-3e - 14$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-7e + 4$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-8e - 1$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}4e - 6$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-8e + 1$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-1$