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

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

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