Properties

Label 5.33.c
Level $5$
Weight $33$
Character orbit 5.c
Rep. character $\chi_{5}(2,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $30$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 33 \)
Character orbit: \([\chi]\) \(=\) 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(5, [\chi])\).

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

Trace form

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

Decomposition of \(S_{33}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.33.c.a \(30\) \(32.433\) None \(-2\) \(-2792232\) \(229266409900\) \(21\!\cdots\!48\)