Properties

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

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
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

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