Properties

Label 7.18.c
Level 7
Weight 18
Character orbit c
Rep. character \(\chi_{7}(2,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 20
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 18 \)
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: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(7, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

Trace form

\( 20q + 270q^{2} + 6560q^{3} - 551660q^{4} + 1089798q^{5} - 1687556q^{6} + 14395360q^{7} - 237823200q^{8} - 498883228q^{9} + O(q^{10}) \) \( 20q + 270q^{2} + 6560q^{3} - 551660q^{4} + 1089798q^{5} - 1687556q^{6} + 14395360q^{7} - 237823200q^{8} - 498883228q^{9} + 222553738q^{10} - 148256184q^{11} + 2808533140q^{12} + 3578734040q^{13} + 25683984606q^{14} - 26900793736q^{15} - 50209759472q^{16} + 15259176570q^{17} + 81764237020q^{18} - 71656970872q^{19} - 180641544216q^{20} - 669146889614q^{21} + 1499692748380q^{22} - 316306503180q^{23} + 694489934496q^{24} + 591325905568q^{25} + 4488505674324q^{26} - 11473086373360q^{27} + 2858273469380q^{28} + 284876854680q^{29} - 9357829097258q^{30} - 1607821082076q^{31} + 18893460602400q^{32} + 9589772011550q^{33} - 32628298247940q^{34} - 103506510744q^{35} + 76724663114416q^{36} + 5528585266950q^{37} - 15690283928010q^{38} + 28451541414128q^{39} - 91022360866896q^{40} - 66727631114424q^{41} - 74393390286880q^{42} - 93028396916240q^{43} + 162849953080692q^{44} + 8592264491540q^{45} - 563088234018354q^{46} + 162460135616460q^{47} + 1626223055746720q^{48} + 37188390461684q^{49} - 156105592028976q^{50} - 41571323179104q^{51} - 664578572037800q^{52} + 349838159677350q^{53} - 2197621449925058q^{54} - 630210277345912q^{55} - 3391192609585536q^{56} + 3387478208982380q^{57} + 1117009291618900q^{58} + 2898325666051656q^{59} + 1851302466771436q^{60} + 4829263771794542q^{61} - 12440234322280740q^{62} + 1252577979478000q^{63} + 2254847316158720q^{64} + 2323606775562324q^{65} + 7963993945620406q^{66} + 1327703510619200q^{67} + 570001815036780q^{68} - 19909363410939516q^{69} - 17777971289904490q^{70} + 15480661755189216q^{71} + 16233423509033760q^{72} - 3163858704730590q^{73} - 4018632851551110q^{74} - 8119026314209112q^{75} - 14641245177256376q^{76} - 46825571816043510q^{77} + 48702643123708840q^{78} + 40826108816616316q^{79} + 90814104963906864q^{80} - 69159481630723930q^{81} + 21247223257167740q^{82} + 10623055038659280q^{83} - 178832833754555092q^{84} + 51769432859611308q^{85} + 113956439761484328q^{86} + 171557044814594000q^{87} - 117726124940340000q^{88} + 31115179936936434q^{89} - 503037784464315176q^{90} - 219799610507722112q^{91} + 208501803198310920q^{92} + 257332309943680890q^{93} + 405400048855155726q^{94} - 22431094320108540q^{95} + 232620528206160416q^{96} - 702800336503765080q^{97} - 760473415304075970q^{98} + 928280307128172080q^{99} + O(q^{100}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.18.c.a \(20\) \(12.826\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(270\) \(6560\) \(1089798\) \(14395360\) \(q+(\beta _{1}+3^{3}\beta _{2})q^{2}+(656-656\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)