# Properties

 Label 4.4.18625.1-9.1-b Base field 4.4.18625.1 Weight $[2, 2, 2, 2]$ Level norm $9$ Level $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ Dimension $7$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.18625.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 14x^{2} + 9x + 41$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ Dimension: $7$ CM: no Base change: no Newspace dimension: $14$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{7} + 4x^{6} - 11x^{5} - 44x^{4} + 42x^{3} + 105x^{2} - 110x + 20$$
Norm Prime Eigenvalue
4 $[4, 2, \frac{1}{6}w^{3} - \frac{7}{3}w - \frac{17}{6}]$ $-\frac{7}{139}e^{6} + \frac{13}{139}e^{5} + \frac{120}{139}e^{4} - \frac{236}{139}e^{3} - \frac{401}{139}e^{2} + \frac{1018}{139}e - \frac{685}{139}$
4 $[4, 2, w - 3]$ $\phantom{-}e$
5 $[5, 5, -\frac{1}{6}w^{3} + w^{2} + \frac{1}{3}w - \frac{25}{6}]$ $-\frac{15}{278}e^{6} + \frac{4}{139}e^{5} + \frac{277}{278}e^{4} - \frac{94}{139}e^{3} - \frac{658}{139}e^{2} + \frac{851}{278}e + \frac{110}{139}$
9 $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $\phantom{-}1$
9 $[9, 3, -w - 2]$ $\phantom{-}\frac{35}{278}e^{6} + \frac{37}{139}e^{5} - \frac{461}{278}e^{4} - \frac{383}{139}e^{3} + \frac{794}{139}e^{2} + \frac{1721}{278}e - \frac{720}{139}$
11 $[11, 11, -\frac{1}{6}w^{3} + \frac{7}{3}w + \frac{11}{6}]$ $\phantom{-}\frac{7}{139}e^{6} - \frac{13}{139}e^{5} - \frac{120}{139}e^{4} + \frac{236}{139}e^{3} + \frac{401}{139}e^{2} - \frac{1157}{139}e + \frac{546}{139}$
11 $[11, 11, -w + 2]$ $\phantom{-}\frac{13}{278}e^{6} - \frac{22}{139}e^{5} - \frac{203}{278}e^{4} + \frac{517}{139}e^{3} + \frac{283}{139}e^{2} - \frac{5167}{278}e + \frac{1341}{139}$
41 $[41, 41, -w]$ $\phantom{-}\frac{113}{278}e^{6} + \frac{322}{139}e^{5} - \frac{567}{278}e^{4} - \frac{3397}{139}e^{3} - \frac{566}{139}e^{2} + \frac{15199}{278}e - \frac{3099}{139}$
41 $[41, 41, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{1}{6}]$ $\phantom{-}\frac{29}{278}e^{6} - \frac{156}{139}e^{5} - \frac{1073}{278}e^{4} + \frac{1998}{139}e^{3} + \frac{2866}{139}e^{2} - \frac{13451}{278}e + \frac{1826}{139}$
59 $[59, 59, -\frac{1}{6}w^{3} + \frac{1}{3}w + \frac{23}{6}]$ $\phantom{-}\frac{18}{139}e^{6} + \frac{185}{139}e^{5} + \frac{168}{139}e^{4} - \frac{1915}{139}e^{3} - \frac{2424}{139}e^{2} + \frac{4372}{139}e + \frac{570}{139}$
59 $[59, 59, -\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{11}{3}]$ $-\frac{187}{278}e^{6} - \frac{293}{139}e^{5} + \frac{1637}{278}e^{4} + \frac{2368}{139}e^{3} - \frac{799}{139}e^{2} - \frac{3087}{278}e - \frac{1455}{139}$
61 $[61, 61, -\frac{5}{3}w^{3} - 3w^{2} + \frac{46}{3}w + \frac{79}{3}]$ $\phantom{-}\frac{57}{278}e^{6} + \frac{235}{139}e^{5} + \frac{115}{278}e^{4} - \frac{2534}{139}e^{3} - \frac{1753}{139}e^{2} + \frac{12779}{278}e - \frac{1669}{139}$
61 $[61, 61, \frac{5}{6}w^{3} + w^{2} - \frac{23}{3}w - \frac{55}{6}]$ $\phantom{-}\frac{53}{139}e^{6} + \frac{120}{139}e^{5} - \frac{710}{139}e^{4} - \frac{1152}{139}e^{3} + \frac{2361}{139}e^{2} + \frac{1645}{139}e - \frac{314}{139}$
61 $[61, 61, w^{3} + 2w^{2} - 9w - 17]$ $\phantom{-}\frac{112}{139}e^{6} + \frac{348}{139}e^{5} - \frac{1225}{139}e^{4} - \frac{3174}{139}e^{3} + \frac{3497}{139}e^{2} + \frac{4562}{139}e - \frac{2384}{139}$
61 $[61, 61, -\frac{1}{6}w^{3} + \frac{10}{3}w + \frac{35}{6}]$ $\phantom{-}\frac{31}{278}e^{6} - \frac{138}{139}e^{5} - \frac{1147}{278}e^{4} + \frac{1714}{139}e^{3} + \frac{3241}{139}e^{2} - \frac{10803}{278}e + \frac{931}{139}$
71 $[71, 71, -\frac{1}{2}w^{3} + 2w^{2} + 4w - \frac{33}{2}]$ $\phantom{-}\frac{15}{139}e^{6} + \frac{131}{139}e^{5} - \frac{138}{139}e^{4} - \frac{1897}{139}e^{3} + \frac{621}{139}e^{2} + \frac{6794}{139}e - \frac{3834}{139}$
71 $[71, 71, \frac{1}{6}w^{3} - w^{2} - \frac{4}{3}w + \frac{67}{6}]$ $-\frac{97}{139}e^{6} - \frac{356}{139}e^{5} + \frac{948}{139}e^{4} + \frac{3362}{139}e^{3} - \frac{2320}{139}e^{2} - \frac{5413}{139}e + \frac{3276}{139}$
79 $[79, 79, \frac{1}{2}w^{3} - 3w + \frac{1}{2}]$ $-\frac{13}{278}e^{6} - \frac{256}{139}e^{5} - \frac{909}{278}e^{4} + \frac{2958}{139}e^{3} + \frac{3748}{139}e^{2} - \frac{15405}{278}e + \frac{605}{139}$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{19}{3}w - \frac{2}{3}]$ $-\frac{227}{278}e^{6} - \frac{375}{139}e^{5} + \frac{2283}{278}e^{4} + \frac{3461}{139}e^{3} - \frac{2600}{139}e^{2} - \frac{10177}{278}e + \frac{1850}{139}$
89 $[89, 89, \frac{1}{2}w^{3} + w^{2} - 5w - \frac{15}{2}]$ $\phantom{-}\frac{38}{139}e^{6} + \frac{267}{139}e^{5} - \frac{155}{139}e^{4} - \frac{2869}{139}e^{3} - \frac{345}{139}e^{2} + \frac{6249}{139}e - \frac{3430}{139}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$9$ $[9, 3, \frac{1}{6}w^{3} - \frac{7}{3}w + \frac{13}{6}]$ $-1$