# Properties

 Label 4.4.19025.1-20.1-e Base field 4.4.19025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, w + 1]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.19025.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 13x^{2} + 14x + 44$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, w + 1]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $35$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 3x^{5} - 14x^{4} - 41x^{3} + 21x^{2} + 70x + 4$$
Norm Prime Eigenvalue
4 $[4, 2, w^{2} - 2w - 6]$ $-\frac{6}{103}e^{5} - \frac{23}{103}e^{4} + \frac{82}{103}e^{3} + \frac{280}{103}e^{2} - \frac{133}{103}e - \frac{239}{103}$
4 $[4, 2, -w^{2} + 7]$ $\phantom{-}1$
5 $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $-1$
5 $[5, 5, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 6w - 9]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{2}w^{3} - 2w^{2} - \frac{5}{2}w + 11]$ $\phantom{-}\frac{6}{103}e^{5} + \frac{23}{103}e^{4} - \frac{82}{103}e^{3} - \frac{280}{103}e^{2} + \frac{30}{103}e + \frac{136}{103}$
11 $[11, 11, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 7]$ $-\frac{10}{103}e^{5} - \frac{4}{103}e^{4} + \frac{171}{103}e^{3} - \frac{14}{103}e^{2} - \frac{565}{103}e + \frac{254}{103}$
31 $[31, 31, \frac{1}{2}w^{2} + \frac{1}{2}w - 4]$ $\phantom{-}\frac{16}{103}e^{5} + \frac{27}{103}e^{4} - \frac{253}{103}e^{3} - \frac{369}{103}e^{2} + \frac{698}{103}e + \frac{88}{103}$
31 $[31, 31, -\frac{1}{2}w^{2} + \frac{3}{2}w + 3]$ $\phantom{-}\frac{6}{103}e^{5} + \frac{23}{103}e^{4} - \frac{82}{103}e^{3} - \frac{280}{103}e^{2} + \frac{30}{103}e + \frac{136}{103}$
41 $[41, 41, \frac{1}{2}w^{2} + \frac{1}{2}w - 6]$ $\phantom{-}\frac{21}{103}e^{5} + \frac{29}{103}e^{4} - \frac{287}{103}e^{3} - \frac{259}{103}e^{2} + \frac{414}{103}e - \frac{142}{103}$
41 $[41, 41, 2w^{3} - \frac{15}{2}w^{2} - \frac{25}{2}w + 50]$ $\phantom{-}\frac{11}{103}e^{5} + \frac{25}{103}e^{4} - \frac{116}{103}e^{3} - \frac{273}{103}e^{2} - \frac{151}{103}e + \frac{112}{103}$
41 $[41, 41, \frac{5}{2}w^{2} - \frac{1}{2}w - 17]$ $\phantom{-}\frac{32}{103}e^{5} + \frac{54}{103}e^{4} - \frac{506}{103}e^{3} - \frac{738}{103}e^{2} + \frac{1396}{103}e + \frac{1206}{103}$
41 $[41, 41, \frac{1}{2}w^{2} - \frac{3}{2}w - 5]$ $-\frac{1}{103}e^{5} - \frac{21}{103}e^{4} - \frac{55}{103}e^{3} + \frac{287}{103}e^{2} + \frac{716}{103}e - \frac{366}{103}$
61 $[61, 61, -\frac{1}{2}w^{3} + w^{2} + \frac{7}{2}w - 1]$ $\phantom{-}\frac{9}{103}e^{5} - \frac{17}{103}e^{4} - \frac{123}{103}e^{3} + \frac{301}{103}e^{2} + \frac{148}{103}e - \frac{826}{103}$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 4w - 3]$ $\phantom{-}\frac{33}{103}e^{5} + \frac{75}{103}e^{4} - \frac{451}{103}e^{3} - \frac{922}{103}e^{2} + \frac{474}{103}e + \frac{542}{103}$
71 $[71, 71, \frac{1}{2}w^{3} + w^{2} - \frac{11}{2}w - 13]$ $-\frac{30}{103}e^{5} - \frac{12}{103}e^{4} + \frac{513}{103}e^{3} + \frac{61}{103}e^{2} - \frac{1695}{103}e - \frac{62}{103}$
71 $[71, 71, -\frac{1}{2}w^{3} + \frac{5}{2}w^{2} + 2w - 17]$ $\phantom{-}\frac{13}{103}e^{5} - \frac{36}{103}e^{4} - \frac{315}{103}e^{3} + \frac{492}{103}e^{2} + \frac{1610}{103}e - \frac{804}{103}$
81 $[81, 3, -3]$ $-\frac{21}{103}e^{5} - \frac{29}{103}e^{4} + \frac{287}{103}e^{3} + \frac{362}{103}e^{2} - \frac{620}{103}e - \frac{682}{103}$
89 $[89, 89, -w^{3} + \frac{3}{2}w^{2} + \frac{13}{2}w - 9]$ $\phantom{-}\frac{15}{103}e^{5} + \frac{6}{103}e^{4} - \frac{308}{103}e^{3} - \frac{82}{103}e^{2} + \frac{1414}{103}e - \frac{278}{103}$
89 $[89, 89, w^{3} - \frac{7}{2}w^{2} - \frac{11}{2}w + 20]$ $-\frac{43}{103}e^{5} - \frac{79}{103}e^{4} + \frac{622}{103}e^{3} + \frac{1011}{103}e^{2} - \frac{1039}{103}e - \frac{1112}{103}$
89 $[89, 89, -w^{3} - \frac{1}{2}w^{2} + \frac{19}{2}w + 12]$ $\phantom{-}\frac{12}{103}e^{5} + \frac{46}{103}e^{4} - \frac{164}{103}e^{3} - \frac{560}{103}e^{2} + \frac{266}{103}e + \frac{478}{103}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -w^{2} + 7]$ $-1$
$5$ $[5, 5, -\frac{1}{2}w^{3} + 2w^{2} + \frac{7}{2}w - 14]$ $1$