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Properties

Label 2.40
Level 2
Weight 40
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 40 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{40}(\Gamma_1(2))\).

Total New Old
Modular forms 11 3 8
Cusp forms 9 3 6
Eisenstein series 2 0 2

Trace form

\( 3 q - 524288 q^{2} - 448040028 q^{3} + 824633720832 q^{4} + 37396559183370 q^{5} - 536281903792128 q^{6} + 23548057401734376 q^{7} - 144115188075855872 q^{8} - 3830161076234277489 q^{9} + O(q^{10}) \) \( 3 q - 524288 q^{2} - 448040028 q^{3} + 824633720832 q^{4} + 37396559183370 q^{5} - 536281903792128 q^{6} + 23548057401734376 q^{7} - 144115188075855872 q^{8} - 3830161076234277489 q^{9} - 36620949074671042560 q^{10} - 600358621179545885364 q^{11} - 123156305123771154432 q^{12} - 2434407943266402155598 q^{13} + 4483749851976880357376 q^{14} + 189447730968003517835640 q^{15} + 226673591177742970257408 q^{16} - 858208600547978241205674 q^{17} - 1674130977592736752336896 q^{18} + 31307516146017089016180 q^{19} + 10279487915232167492321280 q^{20} + 194451182132890125508828896 q^{21} + 139198005730086287975645184 q^{22} + 67157995958368736121296952 q^{23} - 147412047246323721103736832 q^{24} - 33110237710861025700572475 q^{25} - 111659804005730278328762368 q^{26} + 6578752508828661656159145000 q^{27} + 6472840731185912230333906944 q^{28} - 22265174672280926225295581310 q^{29} - 86811803756312046924013240320 q^{30} - 170959699274012182229038580064 q^{31} - 39614081257132168796771975168 q^{32} + 73625213910828578250297519504 q^{33} - 70649380147397247577598459904 q^{34} + 4438918404604032826461134067120 q^{35} - 1052826659893656617564415983616 q^{36} + 388911530082874143587136660906 q^{37} - 12074810088442968904516784619520 q^{38} + 9261643492039898279771447062872 q^{39} - 10066289831948389744219143536640 q^{40} + 68007643161987496150617761700366 q^{41} - 114325973922970028993814447783936 q^{42} + 68986009747378307846115681074412 q^{43} - 165025321205619361393263683567616 q^{44} + 97247126205573429132018612970290 q^{45} - 733815434366087339292749042024448 q^{46} + 915029532778958975491327534903536 q^{47} - 33852947379378837790310749175808 q^{48} + 2992370397058750394122773078750939 q^{49} - 1613910927258641455329291154227200 q^{50} + 945694449303859044594971821681416 q^{51} - 669164960092916523128148052672512 q^{52} - 8066347428099057831850868635343238 q^{53} + 2384237163585732062941288951971840 q^{54} - 8612160318480694923940207312451160 q^{55} + 1232483774571874693314221592018944 q^{56} - 9815465873655629297698789636095120 q^{57} + 57829900979995733731911663621242880 q^{58} - 33000750699110212174217716993073220 q^{59} + 52074995763774818017089696206684160 q^{60} - 149390285509459531187976782625971934 q^{61} + 106232131988115040214806981901287424 q^{62} + 1415461776129972173843762224864392 q^{63} + 62307562302417931542365955950641152 q^{64} + 176906949049275277480139011025791740 q^{65} + 90518311945162978250837339683160064 q^{66} + 26706815503945465585848770020873956 q^{67} - 235902583839967630393470044136800256 q^{68} - 167296225322118915115104888895533408 q^{69} - 2600353600398434685866319608870338560 q^{70} - 605293691077180832680380926385877464 q^{71} - 460181619070804042139150073225805824 q^{72} + 6037896371873457163195986157241568942 q^{73} - 2916112813051584433665890834814337024 q^{74} + 10468531606307457575517562794643194300 q^{75} + 8605744509832662910823290550353920 q^{76} - 3973784746707127600006074129626076768 q^{77} - 3834959291444571989676916960785334272 q^{78} - 3439639541961971841028249340726617200 q^{79} + 2825604122595160296109710638390968320 q^{80} - 20725384932653884806482027979285980997 q^{81} + 18070629096812686567702762098219024384 q^{82} - 57743921443562879954303540675175318348 q^{83} + 53450333947475367361392349925106253824 q^{84} + 12225312483754863430342815668998741620 q^{85} + 46457578983056741804482202317956841472 q^{86} - 65729394324412606646364515839930431720 q^{87} + 38262456465865037447259783025913757696 q^{88} - 166824435684903248525220257650708922370 q^{89} + 8763159135563897597487703355141652480 q^{90} + 198376560035269385711901123618380939376 q^{91} + 18460249363590009545588755068446834688 q^{92} + 406181486152934056717149508202299522944 q^{93} - 225196019506450182093781181208056561664 q^{94} + 58812152031758749530411766655084227800 q^{95} - 40520315005399503255652781877161361408 q^{96} + 615472286923954084663194347601246497766 q^{97} - 2252471551654792460823213172884364591104 q^{98} + 660551890977024558384150004591375044732 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{40}^{\mathrm{new}}(\Gamma_1(2))\)

We only show spaces with even 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
2.40.a \(\chi_{2}(1, \cdot)\) 2.40.a.a 1 1
2.40.a.b 2

Decomposition of \(S_{40}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{40}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{40}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)