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

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

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 \(-2\) \(8\) \(38\) \(-168\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)