Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 18
Level $[18, 6, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w - \frac{4}{3}]$
Label 4.4.18688.1-18.1-d
Dimension 8
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[18, 6, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - 3w - \frac{4}{3}]$
Label 4.4.18688.1-18.1-d
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 28

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut +\mathstrut 4x^{7} \) \(\mathstrut -\mathstrut 27x^{6} \) \(\mathstrut -\mathstrut 117x^{5} \) \(\mathstrut +\mathstrut 133x^{4} \) \(\mathstrut +\mathstrut 843x^{3} \) \(\mathstrut +\mathstrut 673x^{2} \) \(\mathstrut +\mathstrut 6x \) \(\mathstrut -\mathstrut 76\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $-\frac{4052}{86739}e^{7} - \frac{27575}{173478}e^{6} + \frac{231031}{173478}e^{5} + \frac{13981}{2991}e^{4} - \frac{491295}{57826}e^{3} - \frac{996537}{28913}e^{2} - \frac{2279659}{173478}e + \frac{539263}{86739}$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $\phantom{-}1$
9 $[9, 3, w + 1]$ $\phantom{-}\frac{5042}{86739}e^{7} + \frac{30245}{173478}e^{6} - \frac{294199}{173478}e^{5} - \frac{15178}{2991}e^{4} + \frac{690377}{57826}e^{3} + \frac{1065552}{28913}e^{2} + \frac{755797}{173478}e - \frac{661813}{86739}$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{430}{28913}e^{7} + \frac{1456}{28913}e^{6} - \frac{11966}{28913}e^{5} - \frac{1245}{997}e^{4} + \frac{78012}{28913}e^{3} + \frac{213466}{28913}e^{2} + \frac{60700}{28913}e - \frac{60238}{28913}$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}\frac{683}{173478}e^{7} + \frac{3308}{86739}e^{6} - \frac{21965}{173478}e^{5} - \frac{6835}{5982}e^{4} + \frac{51121}{57826}e^{3} + \frac{508031}{57826}e^{2} + \frac{267875}{173478}e - \frac{484292}{86739}$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}\frac{2363}{86739}e^{7} + \frac{6253}{86739}e^{6} - \frac{80819}{86739}e^{5} - \frac{6691}{2991}e^{4} + \frac{242819}{28913}e^{3} + \frac{501610}{28913}e^{2} - \frac{725455}{86739}e - \frac{635086}{86739}$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $-\frac{9151}{173478}e^{7} - \frac{17779}{86739}e^{6} + \frac{268639}{173478}e^{5} + \frac{34367}{5982}e^{4} - \frac{623465}{57826}e^{3} - \frac{2288167}{57826}e^{2} - \frac{1305901}{173478}e + \frac{326764}{86739}$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $-\frac{6859}{86739}e^{7} - \frac{19325}{86739}e^{6} + \frac{204454}{86739}e^{5} + \frac{19523}{2991}e^{4} - \frac{495347}{28913}e^{3} - \frac{1395048}{28913}e^{2} - \frac{387286}{86739}e + \frac{1132058}{86739}$
41 $[41, 41, w^{2} - 5]$ $\phantom{-}\frac{2365}{57826}e^{7} + \frac{4004}{28913}e^{6} - \frac{65813}{57826}e^{5} - \frac{8343}{1994}e^{4} + \frac{342327}{57826}e^{3} + \frac{1810149}{57826}e^{2} + \frac{1519283}{57826}e - \frac{35546}{28913}$
41 $[41, 41, 2w + 3]$ $\phantom{-}\frac{18271}{173478}e^{7} + \frac{29185}{86739}e^{6} - \frac{538567}{173478}e^{5} - \frac{60077}{5982}e^{4} + \frac{1218025}{57826}e^{3} + \frac{4343307}{57826}e^{2} + \frac{4190917}{173478}e - \frac{1366987}{86739}$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $\phantom{-}\frac{7823}{86739}e^{7} + \frac{26758}{86739}e^{6} - \frac{228725}{86739}e^{5} - \frac{27160}{2991}e^{4} + \frac{504425}{28913}e^{3} + \frac{1904707}{28913}e^{2} + \frac{2161322}{86739}e - \frac{375238}{86739}$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $\phantom{-}\frac{2098}{86739}e^{7} + \frac{10039}{173478}e^{6} - \frac{119321}{173478}e^{5} - \frac{5147}{2991}e^{4} + \frac{274057}{57826}e^{3} + \frac{388950}{28913}e^{2} - \frac{91507}{173478}e - \frac{739838}{86739}$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{35093}{173478}e^{7} - \frac{51479}{86739}e^{6} + \frac{1019867}{173478}e^{5} + \frac{104725}{5982}e^{4} - \frac{2297455}{57826}e^{3} - \frac{7451423}{57826}e^{2} - \frac{6170189}{173478}e + \frac{1599479}{86739}$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $\phantom{-}\frac{7445}{173478}e^{7} + \frac{42019}{173478}e^{6} - \frac{101236}{86739}e^{5} - \frac{40951}{5982}e^{4} + \frac{170652}{28913}e^{3} + \frac{2764145}{57826}e^{2} + \frac{2504338}{86739}e - \frac{747740}{86739}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{6734}{86739}e^{7} - \frac{50579}{173478}e^{6} + \frac{405313}{173478}e^{5} + \frac{24946}{2991}e^{4} - \frac{974903}{57826}e^{3} - \frac{1698682}{28913}e^{2} - \frac{1939507}{173478}e + \frac{587389}{86739}$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $-\frac{1257}{28913}e^{7} - \frac{8647}{57826}e^{6} + \frac{75473}{57826}e^{5} + \frac{4393}{997}e^{4} - \frac{517555}{57826}e^{3} - \frac{965996}{28913}e^{2} - \frac{680995}{57826}e + \frac{436846}{28913}$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $\phantom{-}\frac{3475}{173478}e^{7} - \frac{1009}{173478}e^{6} - \frac{46670}{86739}e^{5} + \frac{13}{5982}e^{4} + \frac{90954}{28913}e^{3} + \frac{99875}{57826}e^{2} + \frac{469178}{86739}e + \frac{487154}{86739}$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $\phantom{-}\frac{5465}{173478}e^{7} + \frac{39349}{173478}e^{6} - \frac{69652}{86739}e^{5} - \frac{38557}{5982}e^{4} + \frac{71111}{28913}e^{3} + \frac{2626115}{57826}e^{2} + \frac{3353008}{86739}e - \frac{451712}{86739}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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