# Properties

 Label 4.4.13824.1-1.1-b Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $6$ CM no Base change yes

# Related objects

• L-function not available

## Base field 4.4.13824.1

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

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $6$ CM: no Base change: yes Newspace dimension: $8$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 16x^{4} + 76x^{2} - 92$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}e$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}\frac{1}{2}e^{5} - 5e^{3} + 10e$
11 $[11, 11, -w^{2} + w + 1]$ $-\frac{1}{2}e^{5} + 4e^{3} - 4e$
11 $[11, 11, -w^{2} - w + 1]$ $-\frac{1}{2}e^{5} + 4e^{3} - 4e$
13 $[13, 13, w^{3} - 4w + 1]$ $-e^{4} + 10e^{2} - 20$
13 $[13, 13, -w^{3} + 4w + 1]$ $-e^{4} + 10e^{2} - 20$
25 $[25, 5, -w^{2} - 2w + 1]$ $\phantom{-}2e^{4} - 18e^{2} + 26$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}2e^{4} - 18e^{2} + 26$
37 $[37, 37, w^{3} - 3w - 1]$ $-3e^{4} + 28e^{2} - 46$
37 $[37, 37, w^{3} - 3w + 1]$ $-3e^{4} + 28e^{2} - 46$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} - 6e$
59 $[59, 59, -w^{2} - w + 5]$ $\phantom{-}\frac{1}{2}e^{5} - 3e^{3} - 6e$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}3e^{4} - 28e^{2} + 46$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $\phantom{-}3e^{4} - 28e^{2} + 46$
73 $[73, 73, 2w^{2} - w - 5]$ $\phantom{-}3e^{4} - 24e^{2} + 22$
73 $[73, 73, 2w - 1]$ $\phantom{-}e^{4} - 12e^{2} + 26$
73 $[73, 73, -2w - 1]$ $\phantom{-}e^{4} - 12e^{2} + 26$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}3e^{4} - 24e^{2} + 22$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + 20e$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{3}{2}e^{5} - 14e^{3} + 20e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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