Properties

Label 4.33
Level 4
Weight 33
Dimension 15
Nonzero newspaces 1
Newforms 2
Sturm bound 33
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(33\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(\Gamma_1(4))\).

Total New Old
Modular forms 17 17 0
Cusp forms 15 15 0
Eisenstein series 2 2 0

Trace form

\( 15q + 41756q^{2} + 1372118928q^{4} - 58374617954q^{5} + 1262734959552q^{6} + 90108426597056q^{8} - 9330489743965809q^{9} + O(q^{10}) \) \( 15q + 41756q^{2} + 1372118928q^{4} - 58374617954q^{5} + 1262734959552q^{6} + 90108426597056q^{8} - 9330489743965809q^{9} + 18898036649551416q^{10} - 356375853407619840q^{12} - 310330724778787938q^{13} + 7731597686180285568q^{14} - 12124099049477041920q^{16} + 32998092473679242782q^{17} - 235284708498889038564q^{18} + 1178277970470772776736q^{20} - 2117057333603414716416q^{21} + 5453282318362187158080q^{22} - 25676387438412555666432q^{24} + 25580536411347215174061q^{25} - 13318656836733765948872q^{26} + 287406099989137745118720q^{28} + 79528536198734521127326q^{29} - 58105690536229485525120q^{30} - 1840159638716279585895424q^{32} + 300337698474624477849600q^{33} + 3061726194368939324488248q^{34} + 12017787401329470882617232q^{36} + 2620876359380717116432542q^{37} - 23674230631082905997232960q^{38} - 9024227500247159449524864q^{40} - 81178072464964949049401570q^{41} + 115560171253757823362918400q^{42} - 341183497187317069095824640q^{44} + 442973435281896213295744926q^{45} - 292611965791335032977170048q^{46} + 2221472331677427727192412160q^{48} - 3726696106270429609275304689q^{49} + 493922241360801978941421396q^{50} - 3985635270653999132109697248q^{52} + 11697972364361581520631371422q^{53} + 5640914457354711920825943936q^{54} + 6374003242890184756165527552q^{56} - 45021698676819804378731120640q^{57} - 8194344621477086303654741448q^{58} + 47104092918034241778705984000q^{60} + 35013736512382530415793212830q^{61} + 21568431972603200921875622400q^{62} - 117509138728984201932143357952q^{64} - 148178828737840221416914567108q^{65} + 127488965971714418642064552960q^{66} + 360400933872306679913127653152q^{68} - 518263207562337876647092752384q^{69} - 514873634674652910315035354880q^{70} + 635686255013313098011024741056q^{72} + 2039230631915237097214872797982q^{73} - 108331481302464298617628492232q^{74} - 782627770945775078204519980800q^{76} - 3080015547766001613074070589440q^{77} + 87768417039576149684305430400q^{78} + 2654434108669779778173646414336q^{80} + 3391039348733544470993078655759q^{81} - 12257047852236333596334510646728q^{82} + 18798568063225498187446552682496q^{84} + 6477684469910392785583162643772q^{85} - 23458263349697798020331664550848q^{86} + 11102138256776653733497151431680q^{88} - 1065313629081272451230200381154q^{89} - 49358816481571186295303666931144q^{90} + 60798444498044060215697222361600q^{92} + 43431545808036949970541566115840q^{93} - 130643574777689548682138472237312q^{94} + 345792875639857602943412371832832q^{96} - 117697475906931523308761108394978q^{97} - 387626690825356436327499156699364q^{98} + O(q^{100}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(\Gamma_1(4))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.33.b \(\chi_{4}(3, \cdot)\) 4.33.b.a 1 1
4.33.b.b 14