Properties

Label 7.6.c
Level 7
Weight 6
Character orbit c
Rep. character \(\chi_{7}(2,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(7, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 2q^{2} + 8q^{3} - 12q^{4} + 38q^{5} - 164q^{6} - 168q^{7} + 192q^{8} + 380q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 8q^{3} - 12q^{4} + 38q^{5} - 164q^{6} - 168q^{7} + 192q^{8} + 380q^{9} + 778q^{10} - 424q^{11} + 196q^{12} - 1848q^{13} - 2674q^{14} + 1784q^{15} + 2064q^{16} + 2346q^{17} - 212q^{18} + 360q^{19} - 3416q^{20} - 1526q^{21} + 4252q^{22} + 12q^{23} - 1392q^{24} - 1872q^{25} - 1148q^{26} + 5744q^{27} + 2548q^{28} - 14104q^{29} - 5258q^{30} - 3548q^{31} + 8096q^{32} + 3398q^{33} + 14844q^{34} + 27496q^{35} - 2192q^{36} - 11090q^{37} - 20138q^{38} - 1624q^{39} - 15936q^{40} + 7000q^{41} - 3472q^{42} - 25360q^{43} - 5948q^{44} - 1300q^{45} + 5118q^{46} + 22956q^{47} + 22432q^{48} + 4900q^{49} + 59984q^{50} + 384q^{51} + 1400q^{52} - 3042q^{53} - 32546q^{54} - 50152q^{55} - 57792q^{56} - 38116q^{57} + 58852q^{58} + 65808q^{59} - 14084q^{60} + 42486q^{61} - 98724q^{62} - 4760q^{63} + 70912q^{64} + 3164q^{65} + 25894q^{66} - 42312q^{67} - 5460q^{68} + 10308q^{69} - 113050q^{70} - 4416q^{71} + 32448q^{72} + 50506q^{73} + 47370q^{74} + 35608q^{75} + 77672q^{76} + 65338q^{77} + 55048q^{78} - 9004q^{79} - 68816q^{80} - 51178q^{81} - 67732q^{82} - 208656q^{83} + 44492q^{84} - 106212q^{85} - 86776q^{86} - 80008q^{87} + 20496q^{88} + 26666q^{89} + 261304q^{90} + 135632q^{91} - 20568q^{92} - 38718q^{93} - 98034q^{94} + 198140q^{95} - 54880q^{96} + 418264q^{97} + 98686q^{98} - 133888q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.6.c.a \(4\) \(1.123\) \(\Q(\sqrt{-3}, \sqrt{37})\) None \(-2\) \(8\) \(38\) \(-168\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)