Properties

Label 4.37.b
Level 4
Weight 37
Character orbit b
Rep. character \(\chi_{4}(3,\cdot)\)
Character field \(\Q\)
Dimension 17
Newforms 2
Sturm bound 18
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 37 \)
Character orbit: \([\chi]\) = 4.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(4, [\chi])\).

Total New Old
Modular forms 19 19 0
Cusp forms 17 17 0
Eisenstein series 2 2 0

Trace form

\(17q \) \(\mathstrut -\mathstrut 84916q^{2} \) \(\mathstrut +\mathstrut 63108769040q^{4} \) \(\mathstrut +\mathstrut 1587598983826q^{5} \) \(\mathstrut -\mathstrut 217628996575488q^{6} \) \(\mathstrut -\mathstrut 6116838281275456q^{8} \) \(\mathstrut -\mathstrut 785089825520546847q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(17q \) \(\mathstrut -\mathstrut 84916q^{2} \) \(\mathstrut +\mathstrut 63108769040q^{4} \) \(\mathstrut +\mathstrut 1587598983826q^{5} \) \(\mathstrut -\mathstrut 217628996575488q^{6} \) \(\mathstrut -\mathstrut 6116838281275456q^{8} \) \(\mathstrut -\mathstrut 785089825520546847q^{9} \) \(\mathstrut -\mathstrut 1269669491125656104q^{10} \) \(\mathstrut -\mathstrut 42882825786868930560q^{12} \) \(\mathstrut +\mathstrut 41676149406206500018q^{13} \) \(\mathstrut +\mathstrut 360192888461659120128q^{14} \) \(\mathstrut -\mathstrut 18131657039655345618688q^{16} \) \(\mathstrut +\mathstrut 18678125271466757001058q^{17} \) \(\mathstrut +\mathstrut 98858065961248026757644q^{18} \) \(\mathstrut -\mathstrut 185987631386800333033184q^{20} \) \(\mathstrut -\mathstrut 175281296641396774711296q^{21} \) \(\mathstrut -\mathstrut 4320007363229839528400640q^{22} \) \(\mathstrut +\mathstrut 5118364442017682383085568q^{24} \) \(\mathstrut +\mathstrut 64389827691705544439075331q^{25} \) \(\mathstrut -\mathstrut 30067267580294149817323688q^{26} \) \(\mathstrut -\mathstrut 303534200373547502486016000q^{28} \) \(\mathstrut +\mathstrut 83558829778969622281411570q^{29} \) \(\mathstrut +\mathstrut 361206724962468787334008320q^{30} \) \(\mathstrut +\mathstrut 3424487663300783641955892224q^{32} \) \(\mathstrut -\mathstrut 877278707167997370072668160q^{33} \) \(\mathstrut -\mathstrut 2956121337393437394265165928q^{34} \) \(\mathstrut +\mathstrut 9386969606899626916903182864q^{36} \) \(\mathstrut +\mathstrut 1028936832542213926690666258q^{37} \) \(\mathstrut +\mathstrut 78752216997100984306444174080q^{38} \) \(\mathstrut -\mathstrut 61948625233183002270749961344q^{40} \) \(\mathstrut +\mathstrut 241910655498966263829819397954q^{41} \) \(\mathstrut -\mathstrut 193406458925326074258433843200q^{42} \) \(\mathstrut +\mathstrut 303084904999663560614745692160q^{44} \) \(\mathstrut +\mathstrut 876750889440806776372165555506q^{45} \) \(\mathstrut -\mathstrut 919681205391808405630032112128q^{46} \) \(\mathstrut -\mathstrut 1511312501851283767715389931520q^{48} \) \(\mathstrut -\mathstrut 8690584837344731555055515727247q^{49} \) \(\mathstrut +\mathstrut 10185343958170807211600579472036q^{50} \) \(\mathstrut +\mathstrut 5584769803431310739681792135968q^{52} \) \(\mathstrut +\mathstrut 2864977575306763415468638557778q^{53} \) \(\mathstrut -\mathstrut 42689634574575573966970327785984q^{54} \) \(\mathstrut -\mathstrut 18346492780981997297263940026368q^{56} \) \(\mathstrut -\mathstrut 17591710635767034592583231047680q^{57} \) \(\mathstrut -\mathstrut 13872941779387924373159026137512q^{58} \) \(\mathstrut -\mathstrut 69704584574466315130190074982400q^{60} \) \(\mathstrut +\mathstrut 488044483791787508231294360980594q^{61} \) \(\mathstrut +\mathstrut 406820870675021165265665434183680q^{62} \) \(\mathstrut +\mathstrut 58407051193644631965991706562560q^{64} \) \(\mathstrut -\mathstrut 1419136027205678294994787009303228q^{65} \) \(\mathstrut -\mathstrut 816784109200805225218136599695360q^{66} \) \(\mathstrut +\mathstrut 1913850173378374444103604070923808q^{68} \) \(\mathstrut +\mathstrut 3923547517779842564469076002041856q^{69} \) \(\mathstrut +\mathstrut 312094823977274793710809307489280q^{70} \) \(\mathstrut -\mathstrut 4579322712415668078348091815468096q^{72} \) \(\mathstrut -\mathstrut 7016735948804628395640934715523902q^{73} \) \(\mathstrut -\mathstrut 670997304617426449840386839200808q^{74} \) \(\mathstrut -\mathstrut 15736875982808342938482824299100160q^{76} \) \(\mathstrut +\mathstrut 22639774155764461736245527294259200q^{77} \) \(\mathstrut -\mathstrut 18389491597233550087389536189698560q^{78} \) \(\mathstrut +\mathstrut 47267506511318977155908021422813696q^{80} \) \(\mathstrut -\mathstrut 18188477562036937666899669720078159q^{81} \) \(\mathstrut +\mathstrut 5807936682837544119287618687716888q^{82} \) \(\mathstrut -\mathstrut 37119022564017857733030089777086464q^{84} \) \(\mathstrut -\mathstrut 109102745881421109039130518648221788q^{85} \) \(\mathstrut +\mathstrut 102108696026625816655543232864792832q^{86} \) \(\mathstrut +\mathstrut 39749581676781586144951142033940480q^{88} \) \(\mathstrut +\mathstrut 536580108278993677338741367468283650q^{89} \) \(\mathstrut -\mathstrut 195283296567279720904119484240636584q^{90} \) \(\mathstrut -\mathstrut 17511543929609412714530045318983680q^{92} \) \(\mathstrut -\mathstrut 231978818535002459544922699145134080q^{93} \) \(\mathstrut -\mathstrut 696830931593880576023589572144120832q^{94} \) \(\mathstrut +\mathstrut 1050073689946737522972596709346639872q^{96} \) \(\mathstrut -\mathstrut 467501081650930946766716978739129182q^{97} \) \(\mathstrut +\mathstrut 340279939831197597514188700404039884q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{37}^{\mathrm{new}}(4, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4.37.b.a \(1\) \(32.837\) \(\Q\) \(\Q(\sqrt{-1}) \) \(-262144\) \(0\) \(-4\!\cdots\!34\) \(0\) \(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
4.37.b.b \(16\) \(32.837\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(177228\) \(0\) \(58\!\cdots\!60\) \(0\) \(q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)