Properties

Label 3.39.b
Level 3
Weight 39
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 1
Sturm bound 13
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 39 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(3, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 12 12 0
Eisenstein series 2 2 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 114742404q^{3} \) \(\mathstrut -\mathstrut 1699274528448q^{4} \) \(\mathstrut -\mathstrut 483611204680128q^{6} \) \(\mathstrut +\mathstrut 8107872236538648q^{7} \) \(\mathstrut -\mathstrut 424319151461513940q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 114742404q^{3} \) \(\mathstrut -\mathstrut 1699274528448q^{4} \) \(\mathstrut -\mathstrut 483611204680128q^{6} \) \(\mathstrut +\mathstrut 8107872236538648q^{7} \) \(\mathstrut -\mathstrut 424319151461513940q^{9} \) \(\mathstrut +\mathstrut 8521437485093339520q^{10} \) \(\mathstrut -\mathstrut 2862564534392665536q^{12} \) \(\mathstrut +\mathstrut 1069098773333431501752q^{13} \) \(\mathstrut +\mathstrut 6325133233762551847680q^{15} \) \(\mathstrut +\mathstrut 67078537203201948051456q^{16} \) \(\mathstrut +\mathstrut 1420463738762719667349120q^{18} \) \(\mathstrut -\mathstrut 4607058619794992781108360q^{19} \) \(\mathstrut +\mathstrut 33320142533758881258920952q^{21} \) \(\mathstrut -\mathstrut 136880063896016789094648960q^{22} \) \(\mathstrut +\mathstrut 783927349783175843577206784q^{24} \) \(\mathstrut -\mathstrut 1296747019384761463507120020q^{25} \) \(\mathstrut +\mathstrut 3527882385497241000493515804q^{27} \) \(\mathstrut -\mathstrut 772965222736808266417757568q^{28} \) \(\mathstrut -\mathstrut 31212306699175351074822848640q^{30} \) \(\mathstrut +\mathstrut 62426311865853800230409578584q^{31} \) \(\mathstrut -\mathstrut 201583764927512776992433501440q^{33} \) \(\mathstrut +\mathstrut 279954989831379847783072264704q^{34} \) \(\mathstrut +\mathstrut 524806089486681368742761588544q^{36} \) \(\mathstrut -\mathstrut 1044821541252033349072004239752q^{37} \) \(\mathstrut +\mathstrut 3798009668755107990641466418968q^{39} \) \(\mathstrut -\mathstrut 8640808308189045028871484272640q^{40} \) \(\mathstrut +\mathstrut 3739179021877842175021096471680q^{42} \) \(\mathstrut +\mathstrut 10033244180304067819165288107192q^{43} \) \(\mathstrut -\mathstrut 61618154391458016749088317176320q^{45} \) \(\mathstrut +\mathstrut 133876649746070235210936111300864q^{46} \) \(\mathstrut -\mathstrut 169673882786170669254051959076864q^{48} \) \(\mathstrut -\mathstrut 74274509875804693019854807543452q^{49} \) \(\mathstrut +\mathstrut 717994133339248153525793387369472q^{51} \) \(\mathstrut -\mathstrut 993185387699150183190245387663232q^{52} \) \(\mathstrut +\mathstrut 1237237684228372752705008546718912q^{54} \) \(\mathstrut -\mathstrut 147621918295658178296158670231040q^{55} \) \(\mathstrut -\mathstrut 1942894316331924260346088046339112q^{57} \) \(\mathstrut +\mathstrut 5456952458981587224214732301397120q^{58} \) \(\mathstrut -\mathstrut 21422716753388621512702364409876480q^{60} \) \(\mathstrut +\mathstrut 19261150877798591818539348576756024q^{61} \) \(\mathstrut -\mathstrut 6850204156609697882698173452536488q^{63} \) \(\mathstrut -\mathstrut 3354811274780051137580237339295744q^{64} \) \(\mathstrut +\mathstrut 29491133770268183961996554653096320q^{66} \) \(\mathstrut -\mathstrut 12293160890248249992597347473356552q^{67} \) \(\mathstrut +\mathstrut 14368205812565646738112192879237632q^{69} \) \(\mathstrut +\mathstrut 131887910392782907972479210848551680q^{70} \) \(\mathstrut -\mathstrut 849782187269944662605305038851543040q^{72} \) \(\mathstrut +\mathstrut 904634266610182985560078196407011672q^{73} \) \(\mathstrut -\mathstrut 1950889856240531910659528579515703460q^{75} \) \(\mathstrut +\mathstrut 3737782451304773339414088480976030848q^{76} \) \(\mathstrut -\mathstrut 4783964522796872138966708226773738880q^{78} \) \(\mathstrut +\mathstrut 3380994931932561121624661644777634520q^{79} \) \(\mathstrut -\mathstrut 3842105375893366153709000791027089588q^{81} \) \(\mathstrut +\mathstrut 9707181808332667829526886407699144960q^{82} \) \(\mathstrut -\mathstrut 23112447300276128146951334880402529152q^{84} \) \(\mathstrut +\mathstrut 16191233322474057038450787601892136960q^{85} \) \(\mathstrut -\mathstrut 46435849480387750961684301913616613120q^{87} \) \(\mathstrut +\mathstrut 111257699492994117641050357545187921920q^{88} \) \(\mathstrut -\mathstrut 164148346324517317604081085509260974720q^{90} \) \(\mathstrut +\mathstrut 128973762284915213743998856562037216624q^{91} \) \(\mathstrut -\mathstrut 173596942201215499347713600620947459528q^{93} \) \(\mathstrut +\mathstrut 323629532832623192615016136649966897664q^{94} \) \(\mathstrut -\mathstrut 450074405332355244291177655815409434624q^{96} \) \(\mathstrut +\mathstrut 248679388944018942060778750016570824728q^{97} \) \(\mathstrut -\mathstrut 346605715634587898579110273074604669440q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{39}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.39.b.a \(12\) \(27.439\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-114742404\) \(0\) \(81\!\cdots\!48\) \(q+\beta _{1}q^{2}+(-9561867+97\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)