Properties

Label 1.44.a
Level 1
Weight 44
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 44 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_0(1))\).

Total New Old
Modular forms 4 4 0
Cusp forms 3 3 0
Eisenstein series 1 1 0

Trace form

\(3q \) \(\mathstrut -\mathstrut 2209944q^{2} \) \(\mathstrut +\mathstrut 24401437812q^{3} \) \(\mathstrut +\mathstrut 9822618421824q^{4} \) \(\mathstrut +\mathstrut 535205380774170q^{5} \) \(\mathstrut -\mathstrut 91793974758443424q^{6} \) \(\mathstrut +\mathstrut 301971425665478856q^{7} \) \(\mathstrut -\mathstrut 15830863913787348480q^{8} \) \(\mathstrut +\mathstrut 477482125171066743231q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 2209944q^{2} \) \(\mathstrut +\mathstrut 24401437812q^{3} \) \(\mathstrut +\mathstrut 9822618421824q^{4} \) \(\mathstrut +\mathstrut 535205380774170q^{5} \) \(\mathstrut -\mathstrut 91793974758443424q^{6} \) \(\mathstrut +\mathstrut 301971425665478856q^{7} \) \(\mathstrut -\mathstrut 15830863913787348480q^{8} \) \(\mathstrut +\mathstrut 477482125171066743231q^{9} \) \(\mathstrut +\mathstrut 424411733447436982320q^{10} \) \(\mathstrut +\mathstrut 26665053285822824598396q^{11} \) \(\mathstrut +\mathstrut 591067459530801007163136q^{12} \) \(\mathstrut +\mathstrut 2675160683143344673595682q^{13} \) \(\mathstrut +\mathstrut 14021968617857741064904128q^{14} \) \(\mathstrut +\mathstrut 35619426649405115420082840q^{15} \) \(\mathstrut -\mathstrut 79484355831457348071124992q^{16} \) \(\mathstrut -\mathstrut 408654222932442443796841194q^{17} \) \(\mathstrut -\mathstrut 4107998354973953853903433848q^{18} \) \(\mathstrut +\mathstrut 1577331357975519701176464900q^{19} \) \(\mathstrut +\mathstrut 14558304937461364568422335360q^{20} \) \(\mathstrut +\mathstrut 39305230121617849136195725536q^{21} \) \(\mathstrut +\mathstrut 139626647360508967807005852192q^{22} \) \(\mathstrut -\mathstrut 1215339635928561142484811048q^{23} \) \(\mathstrut -\mathstrut 1116055600560337571570968012800q^{24} \) \(\mathstrut -\mathstrut 2310484082897201607166539950475q^{25} \) \(\mathstrut -\mathstrut 1738302877111230473099097494544q^{26} \) \(\mathstrut +\mathstrut 12636088863973677226324883265480q^{27} \) \(\mathstrut +\mathstrut 16881555000174595924306194912768q^{28} \) \(\mathstrut +\mathstrut 57118989018136587596191009705650q^{29} \) \(\mathstrut -\mathstrut 73851642261923451351367502727360q^{30} \) \(\mathstrut -\mathstrut 255565972342397832812135282963424q^{31} \) \(\mathstrut -\mathstrut 144698056390774688063435943542784q^{32} \) \(\mathstrut -\mathstrut 274896238871162964163796672607216q^{33} \) \(\mathstrut +\mathstrut 460541119788760022406607937310288q^{34} \) \(\mathstrut +\mathstrut 2398213530857285851552147980593520q^{35} \) \(\mathstrut +\mathstrut 8176018057545637654201506848470848q^{36} \) \(\mathstrut -\mathstrut 2320645576165979428293572256842694q^{37} \) \(\mathstrut -\mathstrut 30659398199572233844432077267455520q^{38} \) \(\mathstrut -\mathstrut 3966989860384498209469308423541128q^{39} \) \(\mathstrut -\mathstrut 32703585947405178164040064943232000q^{40} \) \(\mathstrut +\mathstrut 25742376604739002042016577514061166q^{41} \) \(\mathstrut +\mathstrut 142089722887598025677946391121586432q^{42} \) \(\mathstrut +\mathstrut 240714339689128182512406300123419292q^{43} \) \(\mathstrut -\mathstrut 103743099769332204870397943787455232q^{44} \) \(\mathstrut +\mathstrut 257230496455952342677786043056557090q^{45} \) \(\mathstrut -\mathstrut 1897545066442972080018141849284700864q^{46} \) \(\mathstrut +\mathstrut 308713553347399687962182796433367856q^{47} \) \(\mathstrut -\mathstrut 2551621376300181083415582718933352448q^{48} \) \(\mathstrut +\mathstrut 3434980292250886821160584750829904379q^{49} \) \(\mathstrut +\mathstrut 1991781591031845842073119994352349400q^{50} \) \(\mathstrut +\mathstrut 13352566627975131351422398848669478056q^{51} \) \(\mathstrut -\mathstrut 1723278372049486147633277645433304704q^{52} \) \(\mathstrut +\mathstrut 15000497558784669132889458695112796362q^{53} \) \(\mathstrut -\mathstrut 84497407838510132201868358325218843200q^{54} \) \(\mathstrut +\mathstrut 3996571389110251928625895283213506440q^{55} \) \(\mathstrut -\mathstrut 64188456562605926675684864956824883200q^{56} \) \(\mathstrut +\mathstrut 194498189404429212580032012092952587760q^{57} \) \(\mathstrut -\mathstrut 103653602500512241322054964115851073680q^{58} \) \(\mathstrut +\mathstrut 226996261182733939538282061249836505900q^{59} \) \(\mathstrut +\mathstrut 172179025249459513233108554074130526720q^{60} \) \(\mathstrut -\mathstrut 9393429368478033721028929889113591854q^{61} \) \(\mathstrut -\mathstrut 208603081649583360642384119938663534848q^{62} \) \(\mathstrut -\mathstrut 967475285671148246145956691206790781848q^{63} \) \(\mathstrut -\mathstrut 1119010168436659689243622515721507700736q^{64} \) \(\mathstrut -\mathstrut 270218921102297342477494789001032451460q^{65} \) \(\mathstrut +\mathstrut 2927960709398652565212160365298168924032q^{66} \) \(\mathstrut -\mathstrut 733015616887151283726086660162187354444q^{67} \) \(\mathstrut +\mathstrut 5475599618745313926138424496016357744768q^{68} \) \(\mathstrut +\mathstrut 1967042253746083561325124578559972227232q^{69} \) \(\mathstrut +\mathstrut 5947953535225896394715748735968145697920q^{70} \) \(\mathstrut -\mathstrut 18523878066158899993345833814569898287864q^{71} \) \(\mathstrut -\mathstrut 9888656801008664055042728388175401192960q^{72} \) \(\mathstrut -\mathstrut 20251106025908798058937016734369224029298q^{73} \) \(\mathstrut +\mathstrut 16747422277652165725566811926177721225008q^{74} \) \(\mathstrut -\mathstrut 21273380043530396090723723962888745519700q^{75} \) \(\mathstrut +\mathstrut 77507609539490133886259513865936229344000q^{76} \) \(\mathstrut +\mathstrut 59055613160181778232413942942559747685792q^{77} \) \(\mathstrut -\mathstrut 19617648418411520686241571637167142696896q^{78} \) \(\mathstrut +\mathstrut 15233568018599764739559826813006999294800q^{79} \) \(\mathstrut -\mathstrut 100962488695267720109813470111835940986880q^{80} \) \(\mathstrut +\mathstrut 73114835779397486920654645241710822062363q^{81} \) \(\mathstrut -\mathstrut 320808727539069549327137360482471983405168q^{82} \) \(\mathstrut -\mathstrut 89206610196719670053085531955706819434428q^{83} \) \(\mathstrut -\mathstrut 345724182543475881552276196164469715392512q^{84} \) \(\mathstrut +\mathstrut 438725373228516358990025164547060204838420q^{85} \) \(\mathstrut +\mathstrut 251282426033382455934203370485070655838496q^{86} \) \(\mathstrut +\mathstrut 1720273148596604243726575204332689696886840q^{87} \) \(\mathstrut -\mathstrut 25677613216166441601684725395949811087360q^{88} \) \(\mathstrut +\mathstrut 203691422331055117225246388044508249665950q^{89} \) \(\mathstrut -\mathstrut 2339725556415524057280625761410723956665360q^{90} \) \(\mathstrut -\mathstrut 1168954967602248602369466051364648836229584q^{91} \) \(\mathstrut +\mathstrut 688199578839743838535125048241381149958656q^{92} \) \(\mathstrut -\mathstrut 4949189234312030019905814954548842124935296q^{93} \) \(\mathstrut -\mathstrut 1324027207656692012199753325229034662658432q^{94} \) \(\mathstrut +\mathstrut 3125746305909018830165692627580442029979000q^{95} \) \(\mathstrut +\mathstrut 10923904714711076554208778658628955663630336q^{96} \) \(\mathstrut -\mathstrut 3881062021784775072625368160679539917597594q^{97} \) \(\mathstrut +\mathstrut 24120041445786820251814869563279238673540008q^{98} \) \(\mathstrut -\mathstrut 14255275025472043026078170466415579823927508q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.44.a.a \(3\) \(11.711\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-2209944\) \(24401437812\) \(53\!\cdots\!70\) \(30\!\cdots\!56\) \(+\) \(q+(-736648-\beta _{1})q^{2}+(8133812604+\cdots)q^{3}+\cdots\)