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Properties

Label 3.39
Level 3
Weight 39
Dimension 12
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 26
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 39 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(26\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{39}(\Gamma_1(3))\).

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{39}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.39.b \(\chi_{3}(2, \cdot)\) 3.39.b.a 12 1