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Properties

Label 2.36
Level 2
Weight 36
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 36 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(2))\).

Total New Old
Modular forms 10 2 8
Cusp forms 8 2 6
Eisenstein series 2 0 2

Trace form

\( 2 q + 196428600 q^{3} + 34359738368 q^{4} - 2449671719940 q^{5} + 16179410239488 q^{6} - 911971236453200 q^{7} - 73152386550858006 q^{9} + O(q^{10}) \) \( 2 q + 196428600 q^{3} + 34359738368 q^{4} - 2449671719940 q^{5} + 16179410239488 q^{6} - 911971236453200 q^{7} - 73152386550858006 q^{9} - 423075962872135680 q^{10} + 1208140651886483304 q^{11} + 3374617651996262400 q^{12} + 40791498044702598700 q^{13} - 85536603828582875136 q^{14} - 439811992502079968880 q^{15} + 590295810358705651712 q^{16} - 450394234990716966300 q^{17} + 3178098902168292556800 q^{18} + 24090543446664463121560 q^{19} - 42085039692313484328960 q^{20} - 129846333190886892893376 q^{21} + 35240478040671859507200 q^{22} + 318844759828801718883600 q^{23} + 277960151388673951137792 q^{24} + 2389069469849272571022350 q^{25} - 2135372076751279695593472 q^{26} - 15515724648599139357637200 q^{27} - 15667546541836708138188800 q^{28} + 103136265778777057861830540 q^{29} - 61369231394803503448719360 q^{30} + 1267091736301409346752704 q^{31} + 135250823840210691758402400 q^{33} - 1472068537957672521056649216 q^{34} + 2170238489924558529494259360 q^{35} - 1256748431441141506039087104 q^{36} + 4510080673130800660020864700 q^{37} - 5804806241808838609285939200 q^{38} + 3000798417177225993466212048 q^{39} - 7268389697038131901098885120 q^{40} + 3342165486432022025327807604 q^{41} - 15778496049996305117321625600 q^{42} + 22515021111766694100414005800 q^{43} + 20755698355282265980520103936 q^{44} + 50467317878576885543888651820 q^{45} + 86409895677896633258625466368 q^{46} - 449685903278907577700646271200 q^{47} + 57975489807313024488937881600 q^{48} - 128853132594303315270853664814 q^{49} + 1036397221634256193526641459200 q^{50} - 737406927859920616012398544656 q^{51} + 700792600227382429850848460800 q^{52} + 488672473436065298395261532700 q^{53} - 1089127370066902327014960660480 q^{54} - 1913694620239307930912622812880 q^{55} - 1469507664218687354939086209024 q^{56} - 367347627926763431339321359200 q^{57} + 1602368024408844513712904601600 q^{58} + 17202707160809275797256490073480 q^{59} - 7555912496740122713265190993920 q^{60} + 9325615309462610491924196925004 q^{61} - 50503267112815883532252060057600 q^{62} + 25444740726646678062344071206000 q^{63} + 10141204801825835211973625643008 q^{64} - 23669773272076187476693289096280 q^{65} + 13234620499366895847478369714176 q^{66} + 8383444218281090239140729225400 q^{67} - 7737714038368272935403336499200 q^{68} + 72004049599893441412052154967488 q^{69} + 297684854196360356545093875793920 q^{70} - 480139416215308096104875156857296 q^{71} + 54599323393065280078464889651200 q^{72} - 575428513832910713571828858308300 q^{73} + 197969520780653215575049475457024 q^{74} + 722662424222941813825529613592200 q^{75} + 413872384985163957569993090007040 q^{76} - 638623916934338661545063875060800 q^{77} + 120267116816584768674325541683200 q^{78} + 868756140162620235596402706665440 q^{79} - 723015476517393271090766822768640 q^{80} + 1623209532275970217164566535260562 q^{81} - 3526031359697737982401933895270400 q^{82} - 5632023915387843463455844090689000 q^{83} - 2230743018241514120848418940125184 q^{84} + 18677431896998104720787509075727160 q^{85} - 6896184153461153365432717805617152 q^{86} + 10883983710070248948451510541067600 q^{87} + 605426802720367177803722706124800 q^{88} - 25894399503218766762798011514281580 q^{89} + 11581858686292446089528908751831040 q^{90} - 13284449779048054657037283388639456 q^{91} + 5477711263862711765894590522982400 q^{92} - 23656673930604870524334510402374400 q^{93} + 22399861743825587584762263417913344 q^{94} + 41968378729570576408039912200238800 q^{95} + 4775319039222254419775674518601728 q^{96} - 53574180310510263037889481274797500 q^{97} + 78006922355560245621325347107635200 q^{98} - 40929623199791851537753077758145912 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.36.a \(\chi_{2}(1, \cdot)\) 2.36.a.a 1 1
2.36.a.b 1

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)