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

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

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 \(270\) \(6560\) \(1089798\) \(14395360\) \(q+(\beta _{1}+3^{3}\beta _{2})q^{2}+(656-656\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)