# Properties

 Label 4.4.18432.1-4.1-a Base field 4.4.18432.1 Weight $[2, 2, 2, 2]$ Level norm $4$ Level $[4, 2, \frac{1}{3}w^{2} - 2]$ Dimension $4$ CM yes 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: $[4, 2, \frac{1}{3}w^{2} - 2]$ Dimension: $4$ CM: yes Base change: no Newspace dimension: $4$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 8x^{3} - 4x^{2} - 128x - 164$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}0$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}e$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{3}{2}e^{3} - 4e^{2} + 28e + 42$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 10e - 12$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}e^{3} + 3e^{2} - 19e - 38$
9 $[9, 3, w - 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}0$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $\phantom{-}0$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}0$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}0$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}0$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $\phantom{-}0$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}0$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}0$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}0$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}6e^{3} + 17e^{2} - 110e - 186$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-3e^{3} - 9e^{2} + 52e + 102$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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