Properties

Label 2.34
Level 2
Weight 34
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(2))\).

Total New Old
Modular forms 9 3 6
Cusp forms 7 3 4
Eisenstein series 2 0 2

Trace form

\( 3 q + 65536 q^{2} - 124649076 q^{3} + 12884901888 q^{4} + 533466655890 q^{5} + 9264303439872 q^{6} + 99371784824088 q^{7} + 281474976710656 q^{8} + 18852405815679399 q^{9} + O(q^{10}) \) \( 3 q + 65536 q^{2} - 124649076 q^{3} + 12884901888 q^{4} + 533466655890 q^{5} + 9264303439872 q^{6} + 99371784824088 q^{7} + 281474976710656 q^{8} + 18852405815679399 q^{9} - 35660209141186560 q^{10} - 243987735048109404 q^{11} - 535363704896618496 q^{12} + 6127452524374998954 q^{13} + 10883328044408766464 q^{14} - 540011606028256440 q^{15} + 55340232221128654848 q^{16} + 163351956857193229878 q^{17} - 354578147647536955392 q^{18} + 2316286200640058928060 q^{19} + 2291221840554035773440 q^{20} - 10966882762375461396384 q^{21} - 4733220146206274224128 q^{22} - 85544934143271027955896 q^{23} + 39789880294470542426112 q^{24} + 225370380364752475573725 q^{25} + 251615281586057289531392 q^{26} - 743752090411160780985480 q^{27} + 426798565964607073026048 q^{28} - 1885570868915532180931110 q^{29} + 9357659564213453452738560 q^{30} - 6214164899357651844971424 q^{31} + 1208925819614629174706176 q^{32} - 28646531485170550011011952 q^{33} + 28939341541930727759806464 q^{34} - 82084709605255936704167280 q^{35} + 80970466429263222725935104 q^{36} + 19582065655883864004622578 q^{37} + 141223277382323304263843840 q^{38} + 110743367844616772680078248 q^{39} - 153159432029916521834741760 q^{40} + 474990906888239155557354366 q^{41} - 1300079482701292075135008768 q^{42} - 854701774198330191704131836 q^{43} - 1047919342656742876810051584 q^{44} + 7113005491199426978344868970 q^{45} - 3755487355665331416256217088 q^{46} - 3359713735806216538266732912 q^{47} - 2299369603996371501308706816 q^{48} + 1027325841837036133332384171 q^{49} - 8022129800291472803432038400 q^{50} + 34605359459142380076105389016 q^{51} + 26317208199983263347464208384 q^{52} - 25719867322108276836703217886 q^{53} + 65835402527390881086630789120 q^{54} - 203329095921753105019451578920 q^{55} + 46743538022375287618581561344 q^{56} - 246920391711219760108249543440 q^{57} + 90426765572487936244912619520 q^{58} + 486574758853958227127412969780 q^{59} - 2319332187351797861701386240 q^{60} + 8583862334335294799056153146 q^{61} - 158990793629680529653626830848 q^{62} - 91891357726791003768354017736 q^{63} + 237684487542793012780631851008 q^{64} + 1570508277569118621577450564860 q^{65} - 3374590807726680306939142864896 q^{66} + 422874132479815900981844675148 q^{67} + 701591312439247864678620069888 q^{68} + 455702719474062148458385981728 q^{69} - 3024467071475429121489009377280 q^{70} + 5198977231352455543531112459736 q^{71} - 1522901548022430558360050860032 q^{72} - 8030146104418329689734403612706 q^{73} + 13924466895002049051747468836864 q^{74} - 23292509902333321603477068569100 q^{75} + 9948373479925147363530516725760 q^{76} + 27691751685039233175366988812576 q^{77} + 27202320153878090082468855545856 q^{78} - 25638830707110254946114730329360 q^{79} + 9840722873060510167738865418240 q^{80} - 26510678888959286274847485768597 q^{81} - 52988841827294806721870070939648 q^{82} - 53261726130515111552883263441796 q^{83} - 47102402803468745970379772657664 q^{84} - 16465362595617182300874127067580 q^{85} + 51199962022156216766968491671552 q^{86} + 401367777050797863744672651928680 q^{87} - 20329025732724286262637534117888 q^{88} + 99483015972296495211736491705870 q^{89} - 390580869706777575871691707514880 q^{90} + 75577323879611270472141157040976 q^{91} - 367412694483822843534875050377216 q^{92} + 194910148274720557866176228573568 q^{93} + 596297622405425787577101230014464 q^{94} - 943613522324582126565259935432600 q^{95} + 170896234576505829355531536433152 q^{96} + 294906994984199222096704110296358 q^{97} + 934885914868789332728527017541632 q^{98} - 1902504845231598113297079280905132 q^{99} + O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.34.a \(\chi_{2}(1, \cdot)\) 2.34.a.a 1 1
2.34.a.b 2

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)