# Properties

 Label 4.4.7168.1-34.1-e Base field 4.4.7168.1 Weight $[2, 2, 2, 2]$ Level norm $34$ Level $[34, 34, -w - 3]$ 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: $[34, 34, -w - 3]$ Dimension: $3$ CM: no Base change: no Newspace dimension: $12$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{3} + 2x^{2} - 12x - 12$$
Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $\phantom{-}1$
7 $[7, 7, w]$ $\phantom{-}e$
9 $[9, 3, w^{2} + w - 1]$ $-\frac{1}{2}e^{2} - e + 5$
9 $[9, 3, w^{2} - w - 1]$ $\phantom{-}e + 1$
17 $[17, 17, -w^{3} + 3w - 1]$ $\phantom{-}1$
17 $[17, 17, w^{3} - 3w - 1]$ $\phantom{-}e + 2$
23 $[23, 23, -w^{3} - w^{2} + 3w + 4]$ $-\frac{1}{2}e^{2} + 5$
23 $[23, 23, w^{3} - w^{2} - 3w + 4]$ $-e + 4$
41 $[41, 41, w^{3} - w^{2} - 2w + 3]$ $\phantom{-}\frac{1}{2}e^{2} - 5$
41 $[41, 41, -w^{3} - w^{2} + 2w + 3]$ $\phantom{-}e^{2} - e - 12$
49 $[49, 7, w^{2} - 6]$ $\phantom{-}2e$
71 $[71, 71, w^{3} + 3w^{2} - 3w - 6]$ $-e + 4$
71 $[71, 71, -2w^{2} - 2w + 1]$ $\phantom{-}e^{2} + 3e - 4$
73 $[73, 73, w^{2} - 2w - 2]$ $\phantom{-}e - 3$
73 $[73, 73, w^{2} + 2w - 2]$ $\phantom{-}e - 6$
79 $[79, 79, w^{3} - w^{2} - 5w + 2]$ $-e - 1$
79 $[79, 79, -w^{3} - w^{2} + 5w + 2]$ $-e - 4$
89 $[89, 89, 2w - 1]$ $\phantom{-}e^{2} + e - 2$
89 $[89, 89, -2w - 1]$ $\phantom{-}e^{2} - e - 18$
97 $[97, 97, -w^{3} + w^{2} + 4w - 1]$ $-e^{2} - 3e + 14$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,w+1]$ $-1$
$17$ $[17,17,-w^{3}+3w-1]$ $-1$