Properties

Label 5.33.c
Level 5
Weight 33
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 30
Newforms 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: \(\Q(i)\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{33}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

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