Properties

Label 3.21.b
Level 3
Weight 21
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(3, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

Trace form

\(6q \) \(\mathstrut -\mathstrut 4122q^{3} \) \(\mathstrut -\mathstrut 2125200q^{4} \) \(\mathstrut -\mathstrut 96401232q^{6} \) \(\mathstrut +\mathstrut 559607916q^{7} \) \(\mathstrut -\mathstrut 1087483482q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 4122q^{3} \) \(\mathstrut -\mathstrut 2125200q^{4} \) \(\mathstrut -\mathstrut 96401232q^{6} \) \(\mathstrut +\mathstrut 559607916q^{7} \) \(\mathstrut -\mathstrut 1087483482q^{9} \) \(\mathstrut -\mathstrut 10880304480q^{10} \) \(\mathstrut +\mathstrut 63957886128q^{12} \) \(\mathstrut +\mathstrut 17847879276q^{13} \) \(\mathstrut -\mathstrut 487764624960q^{15} \) \(\mathstrut -\mathstrut 317472843648q^{16} \) \(\mathstrut +\mathstrut 9564155313120q^{18} \) \(\mathstrut -\mathstrut 14958020195124q^{19} \) \(\mathstrut +\mathstrut 25978999888044q^{21} \) \(\mathstrut -\mathstrut 71051286019680q^{22} \) \(\mathstrut +\mathstrut 294048705803904q^{24} \) \(\mathstrut -\mathstrut 397204775017050q^{25} \) \(\mathstrut +\mathstrut 1077025592505798q^{27} \) \(\mathstrut -\mathstrut 2034284889273504q^{28} \) \(\mathstrut +\mathstrut 3061064118304800q^{30} \) \(\mathstrut -\mathstrut 2182905165483348q^{31} \) \(\mathstrut +\mathstrut 3811197222014400q^{33} \) \(\mathstrut -\mathstrut 7566372644651136q^{34} \) \(\mathstrut +\mathstrut 6910111676037744q^{36} \) \(\mathstrut -\mathstrut 1934341462168404q^{37} \) \(\mathstrut -\mathstrut 15813602040849876q^{39} \) \(\mathstrut +\mathstrut 44482420967535360q^{40} \) \(\mathstrut -\mathstrut 86552595699685920q^{42} \) \(\mathstrut +\mathstrut 58194987502184076q^{43} \) \(\mathstrut -\mathstrut 81854223046416000q^{45} \) \(\mathstrut +\mathstrut 151411391218915776q^{46} \) \(\mathstrut -\mathstrut 154489681080035712q^{48} \) \(\mathstrut +\mathstrut 188165158287453522q^{49} \) \(\mathstrut -\mathstrut 117657755976045312q^{51} \) \(\mathstrut -\mathstrut 230547517796956704q^{52} \) \(\mathstrut +\mathstrut 489800358305152272q^{54} \) \(\mathstrut -\mathstrut 393208608470140800q^{55} \) \(\mathstrut +\mathstrut 1211071992434087436q^{57} \) \(\mathstrut -\mathstrut 1639827118548168480q^{58} \) \(\mathstrut +\mathstrut 2591328282252814080q^{60} \) \(\mathstrut -\mathstrut 2999109545381544468q^{61} \) \(\mathstrut +\mathstrut 444547436097192876q^{63} \) \(\mathstrut -\mathstrut 83569554960393216q^{64} \) \(\mathstrut +\mathstrut 120735307117251360q^{66} \) \(\mathstrut +\mathstrut 4488155969890198476q^{67} \) \(\mathstrut -\mathstrut 3511312424189451648q^{69} \) \(\mathstrut -\mathstrut 1812568842584740800q^{70} \) \(\mathstrut -\mathstrut 10414532525611288320q^{72} \) \(\mathstrut +\mathstrut 15738405804262597836q^{73} \) \(\mathstrut -\mathstrut 20871070048457840250q^{75} \) \(\mathstrut +\mathstrut 27275280223392575328q^{76} \) \(\mathstrut -\mathstrut 13410777930056987040q^{78} \) \(\mathstrut +\mathstrut 17679940751103803436q^{79} \) \(\mathstrut -\mathstrut 13011625055229011514q^{81} \) \(\mathstrut -\mathstrut 35403353112903693120q^{82} \) \(\mathstrut +\mathstrut 60397598618988279264q^{84} \) \(\mathstrut -\mathstrut 22576574831711316480q^{85} \) \(\mathstrut +\mathstrut 17858271599894295360q^{87} \) \(\mathstrut -\mathstrut 95000209108729447680q^{88} \) \(\mathstrut +\mathstrut 179562325304911301280q^{90} \) \(\mathstrut -\mathstrut 6461010485165713512q^{91} \) \(\mathstrut -\mathstrut 24838278011742494484q^{93} \) \(\mathstrut -\mathstrut 311754310853935072896q^{94} \) \(\mathstrut +\mathstrut 184738040137761352704q^{96} \) \(\mathstrut +\mathstrut 223240336245548394636q^{97} \) \(\mathstrut -\mathstrut 178130031568853028480q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.21.b.a \(6\) \(7.605\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(-4122\) \(0\) \(559607916\) \(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)