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Properties

Label 36.33
Level 36
Weight 33
Dimension 533
Nonzero newspaces 4
Sturm bound 2376
Trace bound 1

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(2376\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(\Gamma_1(36))\).

Total New Old
Modular forms 1172 543 629
Cusp forms 1132 533 599
Eisenstein series 40 10 30

Trace form

\( 533 q + 41757 q^{2} - 24179379 q^{3} - 7262277837 q^{4} + 217526977689 q^{5} + 1021926710799 q^{6} - 56474196874061 q^{7} - 1065320209442694 q^{8} - 1550531549914773 q^{9} + O(q^{10}) \) \( 533 q + 41757 q^{2} - 24179379 q^{3} - 7262277837 q^{4} + 217526977689 q^{5} + 1021926710799 q^{6} - 56474196874061 q^{7} - 1065320209442694 q^{8} - 1550531549914773 q^{9} - 21198702608690904 q^{10} - 38052290352515706 q^{11} + 553156770667006332 q^{12} - 529281227990341775 q^{13} + 5851462869424435620 q^{14} + 2777123272336964775 q^{15} + 1276945630806948495 q^{16} + 144285521556775273242 q^{17} + 467052384456383983752 q^{18} + 41098396198010903158 q^{19} + 164563824751835290572 q^{20} - 2190811027875787161615 q^{21} - 6433995186481974245097 q^{22} + 1286609425798968889551 q^{23} + 10944838414365959713017 q^{24} - 451489209173693202932170 q^{25} + 28301439205699179578100 q^{26} + 136809805741317101222568 q^{27} + 121943266742964746227020 q^{28} + 252388292618379391007397 q^{29} - 398291615556177146635500 q^{30} + 1000296663048223228398613 q^{31} + 6272396918446387238665287 q^{32} - 3630170565726640168821468 q^{33} + 276315066555300657184293 q^{34} + 4561088046395172153226515 q^{36} - 19984003992399722390406014 q^{37} + 53899014205672156414060155 q^{38} - 12654440232728445013210647 q^{39} - 49119017622793734077714196 q^{40} - 34617877655209691157763836 q^{41} + 148010331219832124129919570 q^{42} - 26781677800910723607227408 q^{43} + 181681498051874112749436330 q^{44} - 130071820654556786733501561 q^{45} - 532879766434821480149482344 q^{46} + 1994451365818220610431392119 q^{47} - 3476577230678997676875691917 q^{48} + 16380204067559835779243177964 q^{49} - 1951314123590614657239893343 q^{50} - 8077974459145280861699890197 q^{51} + 11635447829632713733374563286 q^{52} - 12279913068946531110655676262 q^{53} - 33968996474872211136230101431 q^{54} + 32053332232275015207496321098 q^{55} - 52622018455152621815686089810 q^{56} + 60264043079276438701111301241 q^{57} + 24276392830652852524857146028 q^{58} - 42098379479761712968085603256 q^{59} - 103152774654273889751364637272 q^{60} + 66267159844917167129286786097 q^{61} - 126843469220134224226004254140 q^{62} + 104954527927631409322636897809 q^{63} + 284065575462617345002284706242 q^{64} - 765359214341939630627882114679 q^{65} + 853832353196029186489351832610 q^{66} - 6898864073600689948365137102 q^{67} + 523011481200328650241136251947 q^{68} + 1631847825659328404502382292637 q^{69} - 671353836742323509417888315886 q^{70} + 1663374154881448073209126108563 q^{72} - 2314191161133206804864437143464 q^{73} - 5935997431992591681320326198008 q^{74} - 1118326702736163714225122780667 q^{75} - 1151010999482343146146030068771 q^{76} + 1590027615066652811252447021619 q^{77} + 12341709765570483710909619200166 q^{78} - 7924021271866876531651605114293 q^{79} - 18867964159627666247344349413008 q^{80} + 8194472472661030818717703163403 q^{81} + 9406772162340006117756155845998 q^{82} - 18778637674646503170950092004793 q^{83} + 13311911672906649699227033299830 q^{84} - 15796662992015056317640764106626 q^{85} - 19970356829137220591112272902935 q^{86} - 44425645964397874884722808965895 q^{87} + 18809083931756359888181125660683 q^{88} - 105384289037284352334904657231206 q^{89} - 40813959045694077964160569792692 q^{90} + 85454607151854091773532773245018 q^{91} - 22902648311116163876535497619510 q^{92} - 97846629580589421206252270787549 q^{93} + 140114737792475933569641823641108 q^{94} + 272456701875675682791236392068324 q^{95} - 106889781052852626317184973032372 q^{96} - 135920355399988201251970296867266 q^{97} - 410270056193047435662967184944524 q^{98} + 421912678535340390288369769450419 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{33}^{\mathrm{new}}(\Gamma_1(36))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
36.33.c \(\chi_{36}(17, \cdot)\) 36.33.c.a 10 1
36.33.d \(\chi_{36}(19, \cdot)\) 36.33.d.a 1 1
36.33.d.b 14
36.33.d.c 32
36.33.d.d 32
36.33.f \(\chi_{36}(7, \cdot)\) n/a 380 2
36.33.g \(\chi_{36}(5, \cdot)\) 36.33.g.a 64 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{33}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{33}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{33}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{33}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{33}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{33}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{33}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{33}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)