# Properties

 Label 4.4.18432.1-7.1-e 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 $8$ 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: $8$ 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:

 $$x^{8} - 13x^{6} + 54x^{4} - 71x^{2} + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 4]$ $\phantom{-}e$
7 $[7, 7, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 3w - 3]$ $-1$
7 $[7, 7, -\frac{1}{3}w^{2} + w + 1]$ $\phantom{-}e^{2} - 3$
7 $[7, 7, \frac{1}{3}w^{2} + w - 1]$ $-\frac{1}{2}e^{6} + 4e^{4} - 8e^{2} + \frac{9}{2}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 3]$ $-\frac{1}{2}e^{6} + 5e^{4} - 12e^{2} + \frac{5}{2}$
9 $[9, 3, w - 3]$ $-\frac{1}{2}e^{7} + 7e^{5} - 31e^{3} + \frac{87}{2}e$
41 $[41, 41, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w + 1]$ $-e^{7} + 12e^{5} - 47e^{3} + 60e$
41 $[41, 41, -\frac{1}{3}w^{2} + w + 3]$ $\phantom{-}\frac{3}{2}e^{7} - 20e^{5} + 84e^{3} - \frac{215}{2}e$
41 $[41, 41, \frac{1}{3}w^{2} + w - 3]$ $-\frac{3}{2}e^{7} + 17e^{5} - 60e^{3} + \frac{131}{2}e$
41 $[41, 41, -\frac{1}{3}w^{3} - \frac{1}{3}w^{2} + 3w + 1]$ $-\frac{1}{2}e^{7} + 8e^{5} - 38e^{3} + \frac{105}{2}e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 4w - 1]$ $\phantom{-}4e^{5} - 33e^{3} + 63e$
47 $[47, 47, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - 3]$ $-\frac{1}{2}e^{7} + 8e^{5} - 42e^{3} + \frac{141}{2}e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{1}{3}w^{2} - 2w - 3]$ $\phantom{-}2e^{5} - 16e^{3} + 26e$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 4w + 1]$ $\phantom{-}e^{7} - 13e^{5} + 54e^{3} - 70e$
89 $[89, 89, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + 3w - 3]$ $-3e^{7} + 34e^{5} - 118e^{3} + 121e$
89 $[89, 89, \frac{2}{3}w^{2} + w - 5]$ $\phantom{-}\frac{1}{2}e^{7} - 2e^{5} - 13e^{3} + \frac{97}{2}e$
89 $[89, 89, \frac{2}{3}w^{2} - w - 5]$ $\phantom{-}2e^{7} - 23e^{5} + 83e^{3} - 92e$
89 $[89, 89, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - 3]$ $\phantom{-}2e^{7} - 25e^{5} + 100e^{3} - 129e$
97 $[97, 97, \frac{2}{3}w^{3} - \frac{1}{3}w^{2} - 6w + 5]$ $\phantom{-}\frac{1}{2}e^{6} - 4e^{4} + 3e^{2} + \frac{31}{2}$
97 $[97, 97, -w^{3} - \frac{5}{3}w^{2} + 10w + 15]$ $-2e^{6} + 19e^{4} - 45e^{2} + 6$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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