# Properties

 Label 4.4.7168.1-23.1-b Base field 4.4.7168.1 Weight $[2, 2, 2, 2]$ Level norm $23$ Level $[23, 23, -w^{3} - w^{2} + 3w + 4]$ Dimension $8$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.7168.1

Generator $$w$$, with minimal polynomial $$x^{4} - 6x^{2} + 7$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[23, 23, -w^{3} - w^{2} + 3w + 4]$ Dimension: $8$ CM: no Base change: no Newspace dimension: $10$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{8} - 13x^{6} + 51x^{4} - 63x^{2} + 8$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}e$
7 $[7, 7, w]$ $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{21}{4}e^{3} - e$
9 $[9, 3, w^{2} + w - 1]$ $-\frac{1}{2}e^{5} + \frac{9}{2}e^{3} - 8e$
9 $[9, 3, w^{2} - w - 1]$ $-\frac{1}{4}e^{7} + 3e^{5} - \frac{39}{4}e^{3} + 8e$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}e^{3} - 5e$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + \frac{39}{2}e^{3} - 14e$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-1$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $\phantom{-}\frac{1}{4}e^{6} - \frac{5}{2}e^{4} + \frac{25}{4}e^{2} + 2$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $-\frac{1}{4}e^{6} + 2e^{4} - \frac{11}{4}e^{2}$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{5}{2}e^{2} + 2$
49 $[49, 7, w^{2} - 6]$ $-\frac{1}{4}e^{6} + \frac{7}{2}e^{4} - \frac{57}{4}e^{2} + 12$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $-\frac{3}{4}e^{7} + \frac{17}{2}e^{5} - \frac{111}{4}e^{3} + 28e$
71 $[71, 71, -2w^{2} - 2w + 1]$ $\phantom{-}e^{7} - \frac{25}{2}e^{5} + \frac{91}{2}e^{3} - 46e$
73 $[73, 73, w^{2} - 2w - 2]$ $-\frac{1}{4}e^{7} + \frac{5}{2}e^{5} - \frac{25}{4}e^{3} + 2e$
73 $[73, 73, w^{2} + 2w - 2]$ $-\frac{1}{4}e^{7} + \frac{3}{2}e^{5} + \frac{15}{4}e^{3} - 21e$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $\phantom{-}e^{7} - 11e^{5} + 31e^{3} - 21e$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-\frac{1}{4}e^{7} + 3e^{5} - \frac{39}{4}e^{3} + 8e$
89 $[89, 89, 2w - 1]$ $-\frac{1}{4}e^{7} + 3e^{5} - \frac{43}{4}e^{3} + 11e$
89 $[89, 89, -2w - 1]$ $-\frac{1}{2}e^{7} + \frac{15}{2}e^{5} - 36e^{3} + 49e$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $\phantom{-}e^{3} - e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23,23,-w^{3}-w^{2}+3w+4]$ $1$