# Properties

 Label 4.4.13824.1-22.1-d Base field 4.4.13824.1 Weight $[2, 2, 2, 2]$ Level norm $22$ Level $[22, 22, -w^{3} + w^{2} + 3w - 2]$ Dimension $9$ CM no Base change no

# 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: $[22, 22, -w^{3} + w^{2} + 3w - 2]$ Dimension: $9$ CM: no Base change: no Newspace dimension: $26$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{9} - x^{8} - 19x^{7} + 14x^{6} + 119x^{5} - 48x^{4} - 276x^{3} + 13x^{2} + 174x + 36$$
Norm Prime Eigenvalue
2 $[2, 2, -w^{2} + w + 2]$ $\phantom{-}1$
3 $[3, 3, w^{2} - w - 3]$ $\phantom{-}e$
11 $[11, 11, -w^{2} + w + 1]$ $\phantom{-}\frac{1}{8}e^{7} - 2e^{5} + \frac{1}{4}e^{4} + \frac{73}{8}e^{3} - \frac{17}{8}e^{2} - \frac{41}{4}e + \frac{3}{2}$
11 $[11, 11, -w^{2} - w + 1]$ $\phantom{-}1$
13 $[13, 13, w^{3} - 4w + 1]$ $-\frac{1}{24}e^{8} - \frac{1}{12}e^{7} + \frac{2}{3}e^{6} + \frac{11}{12}e^{5} - \frac{77}{24}e^{4} - \frac{11}{8}e^{3} + \frac{9}{2}e^{2} - \frac{11}{3}e + 1$
13 $[13, 13, -w^{3} + 4w + 1]$ $\phantom{-}\frac{1}{12}e^{8} - \frac{5}{24}e^{7} - \frac{4}{3}e^{6} + \frac{19}{6}e^{5} + \frac{20}{3}e^{4} - \frac{109}{8}e^{3} - \frac{101}{8}e^{2} + \frac{193}{12}e + \frac{17}{2}$
25 $[25, 5, -w^{2} - 2w + 1]$ $\phantom{-}\frac{1}{12}e^{8} - \frac{1}{12}e^{7} - \frac{4}{3}e^{6} + \frac{7}{6}e^{5} + \frac{71}{12}e^{4} - \frac{9}{2}e^{3} - \frac{23}{4}e^{2} + \frac{29}{6}e + 1$
25 $[25, 5, w^{2} - 2w - 1]$ $\phantom{-}\frac{1}{12}e^{8} - \frac{1}{12}e^{7} - \frac{11}{6}e^{6} + \frac{7}{6}e^{5} + \frac{155}{12}e^{4} - \frac{9}{2}e^{3} - \frac{117}{4}e^{2} + \frac{13}{3}e + 10$
37 $[37, 37, w^{3} - 3w - 1]$ $-\frac{1}{6}e^{8} + \frac{1}{6}e^{7} + \frac{8}{3}e^{6} - \frac{7}{3}e^{5} - \frac{77}{6}e^{4} + 8e^{3} + \frac{39}{2}e^{2} - \frac{5}{3}e - 2$
37 $[37, 37, w^{3} - 3w + 1]$ $\phantom{-}\frac{1}{12}e^{8} + \frac{1}{24}e^{7} - \frac{4}{3}e^{6} - \frac{5}{6}e^{5} + \frac{37}{6}e^{4} + \frac{37}{8}e^{3} - \frac{63}{8}e^{2} - \frac{65}{12}e + \frac{5}{2}$
59 $[59, 59, w^{2} - w - 5]$ $\phantom{-}\frac{1}{4}e^{7} - 4e^{5} + \frac{1}{2}e^{4} + \frac{77}{4}e^{3} - \frac{17}{4}e^{2} - \frac{55}{2}e + 3$
59 $[59, 59, -w^{2} - w + 5]$ $-\frac{1}{4}e^{8} + \frac{1}{2}e^{7} + \frac{9}{2}e^{6} - \frac{15}{2}e^{5} - \frac{101}{4}e^{4} + \frac{123}{4}e^{3} + \frac{95}{2}e^{2} - \frac{59}{2}e - 21$
61 $[61, 61, -w^{3} + w^{2} + 4w - 7]$ $\phantom{-}\frac{5}{24}e^{8} - \frac{5}{24}e^{7} - \frac{10}{3}e^{6} + \frac{41}{12}e^{5} + \frac{379}{24}e^{4} - \frac{63}{4}e^{3} - \frac{183}{8}e^{2} + \frac{211}{12}e + \frac{17}{2}$
61 $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ $-\frac{1}{24}e^{8} + \frac{1}{24}e^{7} + \frac{7}{6}e^{6} - \frac{13}{12}e^{5} - \frac{239}{24}e^{4} + \frac{31}{4}e^{3} + \frac{231}{8}e^{2} - \frac{161}{12}e - \frac{37}{2}$
73 $[73, 73, 2w^{2} - w - 5]$ $-\frac{1}{8}e^{8} + \frac{1}{2}e^{7} + 2e^{6} - \frac{29}{4}e^{5} - \frac{73}{8}e^{4} + \frac{229}{8}e^{3} + \frac{43}{4}e^{2} - \frac{57}{2}e + 2$
73 $[73, 73, 2w - 1]$ $-\frac{5}{12}e^{8} + \frac{13}{24}e^{7} + \frac{43}{6}e^{6} - \frac{47}{6}e^{5} - \frac{115}{3}e^{4} + \frac{237}{8}e^{3} + \frac{553}{8}e^{2} - \frac{287}{12}e - \frac{49}{2}$
73 $[73, 73, -2w - 1]$ $\phantom{-}\frac{1}{12}e^{8} - \frac{1}{3}e^{7} - \frac{4}{3}e^{6} + \frac{31}{6}e^{5} + \frac{77}{12}e^{4} - \frac{95}{4}e^{3} - \frac{23}{2}e^{2} + \frac{97}{3}e + 10$
73 $[73, 73, 2w^{2} + w - 5]$ $\phantom{-}\frac{1}{8}e^{8} - \frac{1}{2}e^{7} - \frac{5}{2}e^{6} + \frac{29}{4}e^{5} + \frac{129}{8}e^{4} - \frac{221}{8}e^{3} - \frac{141}{4}e^{2} + 20e + 14$
83 $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ $\phantom{-}\frac{1}{8}e^{7} - 2e^{5} + \frac{1}{4}e^{4} + \frac{65}{8}e^{3} - \frac{25}{8}e^{2} - \frac{17}{4}e + \frac{9}{2}$
83 $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{1}{8}e^{8} - \frac{3}{8}e^{7} - 2e^{6} + \frac{25}{4}e^{5} + \frac{83}{8}e^{4} - \frac{61}{2}e^{3} - \frac{183}{8}e^{2} + \frac{161}{4}e + \frac{33}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2,2,-w^{2}+w+2]$ $-1$
$11$ $[11,11,-w^{2}-w+1]$ $-1$