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Properties

Label 7.18.c
Level $7$
Weight $18$
Character orbit 7.c
Rep. character $\chi_{7}(2,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $1$
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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.18.c.a 7.c 7.c $20$ $12.826$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(270\) \(6560\) \(1089798\) \(14395360\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+3^{3}\beta _{2})q^{2}+(656-656\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)