# Properties

 Label 4.4.15188.1-1.1-a Base field 4.4.15188.1 Weight $[2, 2, 2, 2]$ Level norm $1$ Level $[1, 1, 1]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.15188.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + x + 2$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[1, 1, 1]$ Dimension: $6$ 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:

 $$x^{6} - 8x^{4} + 10x^{2} - 1$$
Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, -\frac{1}{2}w^{3} + w^{2} + \frac{3}{2}w]$ $\phantom{-}e^{5} - 8e^{3} + 9e$
11 $[11, 11, \frac{1}{2}w^{3} - w^{2} - \frac{5}{2}w + 4]$ $-e^{4} + 7e^{2} - 4$
11 $[11, 11, -w^{3} + w^{2} + 6w + 1]$ $\phantom{-}2e^{5} - 16e^{3} + 20e$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-e^{5} + 8e^{3} - 9e$
19 $[19, 19, -\frac{1}{2}w^{3} + w^{2} + \frac{5}{2}w]$ $\phantom{-}e^{5} - 8e^{3} + 9e$
23 $[23, 23, -\frac{1}{2}w^{3} + 2w^{2} - \frac{1}{2}w - 2]$ $-e^{4} + 9e^{2} - 10$
31 $[31, 31, -w^{3} + w^{2} + 6w - 1]$ $-4e^{5} + 30e^{3} - 26e$
31 $[31, 31, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-2e^{5} + 14e^{3} - 10e$
43 $[43, 43, \frac{1}{2}w^{3} - w^{2} - \frac{9}{2}w + 2]$ $\phantom{-}3e^{5} - 22e^{3} + 15e$
67 $[67, 67, w^{2} - w - 5]$ $\phantom{-}e^{4} - 5e^{2} - 2$
67 $[67, 67, -\frac{1}{2}w^{3} + \frac{11}{2}w + 2]$ $-2e^{5} + 18e^{3} - 34e$
73 $[73, 73, w^{2} + w + 1]$ $\phantom{-}6$
79 $[79, 79, \frac{1}{2}w^{3} + w^{2} - \frac{5}{2}w - 2]$ $-2e^{4} + 12e^{2} - 2$
81 $[81, 3, -3]$ $\phantom{-}e^{4} - 3e^{2} - 6$
83 $[83, 83, 2w^{3} - 2w^{2} - 12w + 5]$ $\phantom{-}5e^{5} - 38e^{3} + 33e$
83 $[83, 83, -\frac{1}{2}w^{3} - w^{2} + \frac{1}{2}w + 2]$ $-e^{4} + 7e^{2}$
89 $[89, 89, -\frac{3}{2}w^{3} + 2w^{2} + \frac{17}{2}w - 2]$ $-2e^{5} + 16e^{3} - 20e$
89 $[89, 89, \frac{3}{2}w^{3} - 2w^{2} - \frac{21}{2}w + 2]$ $-4e$
97 $[97, 97, \frac{1}{2}w^{3} - w^{2} - \frac{1}{2}w - 2]$ $\phantom{-}2e^{4} - 16e^{2} + 12$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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