# Properties

 Label 4.4.13888.1-1.1-a Base field 4.4.13888.1 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 4.4.13888.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 6x + 9$$; 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: $6$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} - 36x^{4} + 264x^{2} - 256$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $-\frac{1}{24}e^{4} + \frac{4}{3}e^{2} - \frac{14}{3}$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{1}{48}e^{5} + \frac{2}{3}e^{3} - \frac{23}{6}e$
7 $[7, 7, w - 2]$ $\phantom{-}e$
7 $[7, 7, w - 1]$ $-\frac{1}{48}e^{5} + \frac{2}{3}e^{3} - \frac{23}{6}e$
9 $[9, 3, w]$ $-\frac{1}{96}e^{5} + \frac{11}{24}e^{3} - \frac{53}{12}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $-\frac{1}{96}e^{5} + \frac{11}{24}e^{3} - \frac{53}{12}e$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - 8$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $\phantom{-}\frac{1}{2}e^{2} - 8$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $\phantom{-}\frac{1}{12}e^{4} - \frac{8}{3}e^{2} + \frac{40}{3}$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $\phantom{-}\frac{1}{32}e^{5} - \frac{9}{8}e^{3} + \frac{25}{4}e$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $\phantom{-}\frac{1}{32}e^{5} - \frac{9}{8}e^{3} + \frac{25}{4}e$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $-\frac{1}{16}e^{5} + 2e^{3} - \frac{17}{2}e$
47 $[47, 47, w^{2} - w - 4]$ $-\frac{1}{16}e^{5} + 2e^{3} - \frac{17}{2}e$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $\phantom{-}\frac{1}{96}e^{5} - \frac{11}{24}e^{3} + \frac{65}{12}e$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-\frac{1}{6}e^{4} + \frac{13}{3}e^{2} - \frac{44}{3}$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $-\frac{1}{6}e^{4} + \frac{13}{3}e^{2} - \frac{44}{3}$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $\phantom{-}\frac{1}{96}e^{5} - \frac{11}{24}e^{3} + \frac{65}{12}e$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}\frac{5}{48}e^{5} - \frac{10}{3}e^{3} + \frac{91}{6}e$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $\phantom{-}\frac{5}{48}e^{5} - \frac{10}{3}e^{3} + \frac{91}{6}e$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $-\frac{1}{32}e^{5} + \frac{7}{8}e^{3} - \frac{5}{4}e$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

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