# Properties

 Label 4.4.13025.1-20.2-h Base field 4.4.13025.1 Weight $[2, 2, 2, 2]$ Level norm $20$ Level $[20, 10, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{5}{4}]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13025.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 12x^{2} + 3x + 29$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[20, 10, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{5}{4}]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $19$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} - 3x^{6} - 23x^{5} + 69x^{4} + 136x^{3} - 404x^{2} - 192x + 576$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $\phantom{-}1$
4 $[4, 2, -w^{2} + w + 8]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $\phantom{-}1$
5 $[5, 5, \frac{1}{2}w^{3} - w^{2} - 4w + \frac{9}{2}]$ $-\frac{5}{288}e^{6} + \frac{1}{96}e^{5} + \frac{151}{288}e^{4} - \frac{23}{96}e^{3} - \frac{305}{72}e^{2} + \frac{97}{72}e + \frac{43}{6}$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{21}{4}]$ $-\frac{35}{288}e^{6} + \frac{7}{96}e^{5} + \frac{769}{288}e^{4} - \frac{161}{96}e^{3} - \frac{1055}{72}e^{2} + \frac{463}{72}e + \frac{103}{6}$
19 $[19, 19, \frac{1}{4}w^{3} - \frac{3}{2}w^{2} - \frac{1}{2}w + \frac{41}{4}]$ $\phantom{-}\frac{1}{36}e^{6} + \frac{1}{12}e^{5} - \frac{23}{36}e^{4} - \frac{17}{12}e^{3} + \frac{34}{9}e^{2} + \frac{71}{18}e - \frac{8}{3}$
29 $[29, 29, w]$ $\phantom{-}\frac{7}{96}e^{6} - \frac{3}{32}e^{5} - \frac{149}{96}e^{4} + \frac{53}{32}e^{3} + \frac{193}{24}e^{2} - \frac{95}{24}e - \frac{13}{2}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{1}{2}w + \frac{1}{4}]$ $-\frac{17}{144}e^{6} + \frac{1}{48}e^{5} + \frac{391}{144}e^{4} - \frac{23}{48}e^{3} - \frac{307}{18}e^{2} + \frac{13}{36}e + \frac{85}{3}$
29 $[29, 29, \frac{1}{4}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + \frac{9}{4}]$ $-\frac{7}{144}e^{6} - \frac{1}{48}e^{5} + \frac{161}{144}e^{4} - \frac{1}{48}e^{3} - \frac{137}{18}e^{2} + \frac{89}{36}e + \frac{47}{3}$
29 $[29, 29, -\frac{1}{2}w^{3} + w^{2} + 4w - \frac{5}{2}]$ $\phantom{-}\frac{11}{96}e^{6} + \frac{1}{32}e^{5} - \frac{265}{96}e^{4} - \frac{23}{32}e^{3} + \frac{443}{24}e^{2} + \frac{113}{24}e - \frac{63}{2}$
41 $[41, 41, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{47}{4}]$ $-\frac{1}{24}e^{6} + \frac{1}{8}e^{5} + \frac{35}{24}e^{4} - \frac{19}{8}e^{3} - \frac{79}{6}e^{2} + \frac{28}{3}e + 24$
41 $[41, 41, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{15}{4}]$ $\phantom{-}\frac{1}{48}e^{6} - \frac{1}{16}e^{5} - \frac{47}{48}e^{4} + \frac{15}{16}e^{3} + \frac{34}{3}e^{2} - \frac{35}{12}e - 27$
61 $[61, 61, -\frac{3}{2}w^{3} + 3w^{2} + 11w - \frac{21}{2}]$ $\phantom{-}\frac{17}{288}e^{6} - \frac{13}{96}e^{5} - \frac{283}{288}e^{4} + \frac{251}{96}e^{3} + \frac{173}{72}e^{2} - \frac{625}{72}e + \frac{17}{6}$
61 $[61, 61, w^{3} - 2w^{2} - 4w + 6]$ $-\frac{19}{144}e^{6} - \frac{1}{48}e^{5} + \frac{473}{144}e^{4} + \frac{23}{48}e^{3} - \frac{817}{36}e^{2} - \frac{157}{36}e + \frac{113}{3}$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{5}{2}w^{2} - \frac{7}{2}w + \frac{27}{4}]$ $-\frac{31}{288}e^{6} + \frac{11}{96}e^{5} + \frac{749}{288}e^{4} - \frac{205}{96}e^{3} - \frac{1189}{72}e^{2} + \frac{551}{72}e + \frac{131}{6}$
79 $[79, 79, \frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{5}{2}w - \frac{35}{4}]$ $\phantom{-}\frac{5}{72}e^{6} - \frac{7}{24}e^{5} - \frac{133}{72}e^{4} + \frac{125}{24}e^{3} + \frac{511}{36}e^{2} - \frac{152}{9}e - \frac{80}{3}$
81 $[81, 3, -3]$ $-\frac{11}{96}e^{6} - \frac{1}{32}e^{5} + \frac{265}{96}e^{4} - \frac{9}{32}e^{3} - \frac{443}{24}e^{2} + \frac{151}{24}e + \frac{59}{2}$
89 $[89, 89, \frac{7}{4}w^{3} - \frac{11}{2}w^{2} - \frac{21}{2}w + \frac{119}{4}]$ $-\frac{35}{288}e^{6} + \frac{7}{96}e^{5} + \frac{913}{288}e^{4} - \frac{113}{96}e^{3} - \frac{1667}{72}e^{2} + \frac{67}{72}e + \frac{265}{6}$
89 $[89, 89, \frac{1}{4}w^{3} + \frac{3}{2}w^{2} - \frac{3}{2}w - \frac{23}{4}]$ $\phantom{-}\frac{25}{288}e^{6} - \frac{5}{96}e^{5} - \frac{611}{288}e^{4} + \frac{163}{96}e^{3} + \frac{1057}{72}e^{2} - \frac{593}{72}e - \frac{173}{6}$
109 $[109, 109, -\frac{1}{2}w^{3} + 3w^{2} + 2w - \frac{41}{2}]$ $-\frac{35}{144}e^{6} + \frac{7}{48}e^{5} + \frac{769}{144}e^{4} - \frac{161}{48}e^{3} - \frac{1091}{36}e^{2} + \frac{427}{36}e + \frac{127}{3}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, \frac{1}{2}w^{3} - 2w^{2} - 2w + \frac{15}{2}]$ $-1$
$5$ $[5, 5, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{1}{2}w - \frac{9}{4}]$ $-1$