# Properties

 Label 4.4.7168.1-18.1-b Base field 4.4.7168.1 Weight $[2, 2, 2, 2]$ Level norm $18$ Level $[18, 6, -w^{2} - w + 4]$ Dimension $3$ 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: $[18, 6, -w^{2} - w + 4]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + x^{2} - 11x - 14$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
9 $[9, 3, w^{2} + w - 1]$ $-1$
9 $[9, 3, w^{2} - w - 1]$ $\phantom{-}e^{2} - 6$
17 $[17, 17, -w^{3} + 3w - 1]$ $-2e$
17 $[17, 17, w^{3} - 3w - 1]$ $-e^{2} + 2e + 11$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $\phantom{-}e^{2} - 6$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $-e^{2} + e + 11$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $\phantom{-}e^{2} - 2e - 4$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $-e$
49 $[49, 7, w^{2} - 6]$ $-e^{2} + 2e + 11$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $\phantom{-}e^{2} + e - 9$
71 $[71, 71, -2w^{2} - 2w + 1]$ $\phantom{-}e^{2} - 2e - 16$
73 $[73, 73, w^{2} - 2w - 2]$ $-3e^{2} + 3e + 23$
73 $[73, 73, w^{2} + 2w - 2]$ $\phantom{-}e^{2} - 2$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $-e^{2} + 1$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-2e + 6$
89 $[89, 89, 2w - 1]$ $\phantom{-}e^{2} - e - 9$
89 $[89, 89, -2w - 1]$ $-e^{2} - e + 17$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $-2e^{2} - 2e + 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,w+1]$ $1$
$9$ $[9,3,w^{2}+w-1]$ $1$