# Properties

 Label 4.4.18432.1-1.1-a Base field 4.4.18432.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $4$ CM no Base change yes

# 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: $[1, 1, 1]$ Dimension: $4$ CM: no Base change: yes Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 4x^{3} - 28x^{2} - 64x - 8$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{13}{5}e - \frac{14}{5}$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{10}e^{3} - \frac{3}{10}e^{2} + \frac{18}{5}e + \frac{24}{5}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $\phantom{-}\frac{1}{10}e^{3} + \frac{3}{10}e^{2} - \frac{18}{5}e - \frac{14}{5}$
9 $[9, 3, w - 3]$ $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{26}{5}e + \frac{28}{5}$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-\frac{1}{10}e^{3} - \frac{4}{5}e^{2} + \frac{8}{5}e + \frac{54}{5}$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{1}{10}e^{3} + \frac{1}{5}e^{2} + \frac{18}{5}e - \frac{26}{5}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{26}{5}e - \frac{28}{5}$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $-\frac{2}{5}e^{3} - \frac{6}{5}e^{2} + \frac{52}{5}e + \frac{56}{5}$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}\frac{1}{5}e^{3} + \frac{3}{5}e^{2} - \frac{36}{5}e - \frac{48}{5}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-\frac{1}{5}e^{3} - \frac{3}{5}e^{2} + \frac{36}{5}e + \frac{28}{5}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is $$(1)$$.