Properties

Label 5.33
Level 5
Weight 33
Dimension 30
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 66
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 33 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(66\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(\Gamma_1(5))\).

Total New Old
Modular forms 34 34 0
Cusp forms 30 30 0
Eisenstein series 4 4 0

Trace form

\( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8} + O(q^{10}) \) \( 30 q - 2 q^{2} - 2792232 q^{3} + 229266409900 q^{5} - 645476451240 q^{6} + 21807690136848 q^{7} + 340768936037220 q^{8} - 17555754485145450 q^{10} - 60908362837533640 q^{11} + 444566273630869608 q^{12} + 649759187023107138 q^{13} + 6285624407445962400 q^{15} - 46108906958970522120 q^{16} - 218107661739005884502 q^{17} + 240407468159884203858 q^{18} - 3053538044199826052700 q^{20} + 4549905652154594876760 q^{21} - 11386561172247365212944 q^{22} + 13896091629970965206008 q^{23} + 35772470267692728866250 q^{25} - 23129486500762683557740 q^{26} + 176388356775702789525960 q^{27} + 59665474478272755491112 q^{28} + 1233340129583886997444800 q^{30} - 1285786827516670637255040 q^{31} + 3122517776856150857591368 q^{32} - 1644615516923295701112504 q^{33} - 818578197767771892231200 q^{35} + 31947551193266858523505980 q^{36} - 126275105375668809211002 q^{37} + 57601564734016178366855880 q^{38} + 211125410957683032210619500 q^{40} - 155417315271390260892986440 q^{41} + 797836438482097707185724336 q^{42} - 545147034084978191886568152 q^{43} + 1085165439164371861108713450 q^{45} - 3454637097270705106900721640 q^{46} + 2735203198488492729395621848 q^{47} - 3192952350241941373327314192 q^{48} + 4470181549725126255525651250 q^{50} - 6129415060408014316542923040 q^{51} + 6000870590399837156109494028 q^{52} - 11282171275183571262774628682 q^{53} - 7112951743928365540876222200 q^{55} - 47918174764291639802549158800 q^{56} + 44765351794015370451647799120 q^{57} - 29637988346430122895588672480 q^{58} + 34183609322952768706653073800 q^{60} + 50784540875895586667393303160 q^{61} - 218235799024898727529128868024 q^{62} + 213794735887989269330759842008 q^{63} - 349686192916613591890379914850 q^{65} + 1348836243659025586642346421120 q^{66} - 736483403252315334072161239752 q^{67} + 1085395947449178489054935855012 q^{68} - 363042164247863030846151545400 q^{70} + 817740403780342392034746361760 q^{71} - 951267702824572414087545605820 q^{72} - 379868722209495311437504600242 q^{73} + 104600806158947004257336610000 q^{75} - 6689750080738358201358794259600 q^{76} + 6381539826853244422672988941256 q^{77} - 9179143477318522110451614982584 q^{78} + 5875581782593356038176152810400 q^{80} - 14239669107938661073624705472070 q^{81} + 2725313872720345364461277817936 q^{82} + 4996401755555614465785455997328 q^{83} - 4438937659194362238905211673950 q^{85} + 16049932109847278395442966171960 q^{86} + 36834415428157346041110451524480 q^{87} - 47132513308908068698430156048160 q^{88} + 81433975991640870510397972968150 q^{90} - 104150500668224029090357708737840 q^{91} - 18747876848872687606754750486552 q^{92} + 112210213536624471769268225064216 q^{93} - 109796172349696400850071817591000 q^{95} + 380819283905835347723966665116960 q^{96} - 155781506757725945270376012026802 q^{97} + 125692870459469366775669291878702 q^{98} + O(q^{100}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.33.c \(\chi_{5}(2, \cdot)\) 5.33.c.a 30 2