Properties

Label 1.46.a
Level 1
Weight 46
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: \( k \) = \( 46 \)
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 \(M_{46}(\Gamma_0(1))\).

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

Trace form

\(3q \) \(\mathstrut +\mathstrut 3814272q^{2} \) \(\mathstrut +\mathstrut 5359866876q^{3} \) \(\mathstrut -\mathstrut 1915164893184q^{4} \) \(\mathstrut -\mathstrut 912448458460350q^{5} \) \(\mathstrut -\mathstrut 84402581069044224q^{6} \) \(\mathstrut -\mathstrut 7619710926638056008q^{7} \) \(\mathstrut -\mathstrut 108947667758662287360q^{8} \) \(\mathstrut +\mathstrut 1158701600689591796919q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 3814272q^{2} \) \(\mathstrut +\mathstrut 5359866876q^{3} \) \(\mathstrut -\mathstrut 1915164893184q^{4} \) \(\mathstrut -\mathstrut 912448458460350q^{5} \) \(\mathstrut -\mathstrut 84402581069044224q^{6} \) \(\mathstrut -\mathstrut 7619710926638056008q^{7} \) \(\mathstrut -\mathstrut 108947667758662287360q^{8} \) \(\mathstrut +\mathstrut 1158701600689591796919q^{9} \) \(\mathstrut +\mathstrut 1419132609182896876800q^{10} \) \(\mathstrut -\mathstrut 292602117773160656797644q^{11} \) \(\mathstrut -\mathstrut 3364742928052149867675648q^{12} \) \(\mathstrut -\mathstrut 24359353574857845965202054q^{13} \) \(\mathstrut -\mathstrut 202717255077168503234024448q^{14} \) \(\mathstrut -\mathstrut 1135189552611303064861248600q^{15} \) \(\mathstrut -\mathstrut 2516639057595474468963090432q^{16} \) \(\mathstrut +\mathstrut 1167342337360426664689201782q^{17} \) \(\mathstrut +\mathstrut 29579133880859462479907669376q^{18} \) \(\mathstrut +\mathstrut 139928385765722236845372310380q^{19} \) \(\mathstrut +\mathstrut 381381185200730248341345484800q^{20} \) \(\mathstrut +\mathstrut 2269674947269963115109120096q^{21} \) \(\mathstrut -\mathstrut 3645081261141863565639576301056q^{22} \) \(\mathstrut -\mathstrut 10673923189590823281275419815384q^{23} \) \(\mathstrut -\mathstrut 10660038263992615442172723855360q^{24} \) \(\mathstrut +\mathstrut 43966129876780298643382415638125q^{25} \) \(\mathstrut +\mathstrut 109857986164645419011108420802816q^{26} \) \(\mathstrut +\mathstrut 286662461859179128178856521495640q^{27} \) \(\mathstrut +\mathstrut 5309187993026577435829326249984q^{28} \) \(\mathstrut -\mathstrut 670860386246579691273176792023830q^{29} \) \(\mathstrut -\mathstrut 4402953564890863333453835153587200q^{30} \) \(\mathstrut -\mathstrut 4362750588615761992088215111558944q^{31} \) \(\mathstrut +\mathstrut 2770584927822325193163626168451072q^{32} \) \(\mathstrut +\mathstrut 32665703367813314965816678845383952q^{33} \) \(\mathstrut +\mathstrut 53874322809182721932452359249215232q^{34} \) \(\mathstrut +\mathstrut 15776204147695493575553971787662800q^{35} \) \(\mathstrut -\mathstrut 102525010025813312391010920028741632q^{36} \) \(\mathstrut -\mathstrut 389811033762613666259144433874550238q^{37} \) \(\mathstrut -\mathstrut 298309080939187021552909089031242240q^{38} \) \(\mathstrut -\mathstrut 409236468450733544586776272530045432q^{39} \) \(\mathstrut +\mathstrut 1418999553421731071561941465300992000q^{40} \) \(\mathstrut +\mathstrut 2715552056267791317916826925062933406q^{41} \) \(\mathstrut +\mathstrut 5586686494853964635832792594060570624q^{42} \) \(\mathstrut +\mathstrut 1244478438653295151469201253707220756q^{43} \) \(\mathstrut -\mathstrut 10866498414076105454653552938468999168q^{44} \) \(\mathstrut -\mathstrut 36806221258052298400850661208655540550q^{45} \) \(\mathstrut -\mathstrut 29420915174298432781096019434857298944q^{46} \) \(\mathstrut -\mathstrut 5368746178058366301880916464880208048q^{47} \) \(\mathstrut +\mathstrut 148508904948621262654306355588068540416q^{48} \) \(\mathstrut +\mathstrut 78160841959900415140960388420190127371q^{49} \) \(\mathstrut +\mathstrut 365636939507033508238037233476615120000q^{50} \) \(\mathstrut -\mathstrut 373116254852470180408674865132312910664q^{51} \) \(\mathstrut +\mathstrut 134213023925843531561035140325636718592q^{52} \) \(\mathstrut -\mathstrut 1852254617049027724838330153197946097774q^{53} \) \(\mathstrut +\mathstrut 598319193424014381333123622203435924480q^{54} \) \(\mathstrut -\mathstrut 3433604438201040460840734686798586808200q^{55} \) \(\mathstrut +\mathstrut 5263223929490768485344096600823148052480q^{56} \) \(\mathstrut +\mathstrut 103199557648847905550120265832946125680q^{57} \) \(\mathstrut +\mathstrut 13570181249555445898814714558437144899840q^{58} \) \(\mathstrut -\mathstrut 3587009869064273690797416085301514120060q^{59} \) \(\mathstrut +\mathstrut 13404510441959335634932360628989029580800q^{60} \) \(\mathstrut -\mathstrut 51762384161673790814764907347052617635894q^{61} \) \(\mathstrut -\mathstrut 5676710491956141755174145478721599328256q^{62} \) \(\mathstrut -\mathstrut 63198441434102160493715367231351517178664q^{63} \) \(\mathstrut +\mathstrut 41050065173647728685920731234203689025536q^{64} \) \(\mathstrut +\mathstrut 37939089079008549181090608539522846859900q^{65} \) \(\mathstrut +\mathstrut 225875143847752677055610226576839213770752q^{66} \) \(\mathstrut +\mathstrut 14148137855196379836825399018252188940732q^{67} \) \(\mathstrut +\mathstrut 123753416143995711246382651604664796299264q^{68} \) \(\mathstrut -\mathstrut 91367025965579022204230939913277492454112q^{69} \) \(\mathstrut -\mathstrut 615758273709518152674920733006194538854400q^{70} \) \(\mathstrut -\mathstrut 125388248998914140052658001286881482385544q^{71} \) \(\mathstrut -\mathstrut 1156126662482217982994085922934573149716480q^{72} \) \(\mathstrut +\mathstrut 545662435246745842274304841909717562787966q^{73} \) \(\mathstrut -\mathstrut 922589101552630918194661534146849410212608q^{74} \) \(\mathstrut +\mathstrut 4696791604551172366648127047375667988322500q^{75} \) \(\mathstrut -\mathstrut 25740309904677479085695622290576752803840q^{76} \) \(\mathstrut +\mathstrut 6645319565466313145724427222526529624900384q^{77} \) \(\mathstrut -\mathstrut 4595509600825448911666359841694663296601088q^{78} \) \(\mathstrut +\mathstrut 906179897072215837642402032445458679683120q^{79} \) \(\mathstrut -\mathstrut 16837014550545085717858942703269209282969600q^{80} \) \(\mathstrut -\mathstrut 10433460971272354761639583481407161767228277q^{81} \) \(\mathstrut -\mathstrut 7077813252702994823298504428501096216345856q^{82} \) \(\mathstrut +\mathstrut 1486742880234689875145309838364765216168236q^{83} \) \(\mathstrut +\mathstrut 28631042844956213576694159923345730259648512q^{84} \) \(\mathstrut +\mathstrut 38251451691354483777201487197950382555147300q^{85} \) \(\mathstrut +\mathstrut 49387084957597704283946327082198769274651136q^{86} \) \(\mathstrut -\mathstrut 19149930875978892871878601194088020234221880q^{87} \) \(\mathstrut +\mathstrut 52989682432050008057661862219403039374049280q^{88} \) \(\mathstrut -\mathstrut 157452314112877728949303270670086721758716690q^{89} \) \(\mathstrut -\mathstrut 34876870282343920020702397831481807365113600q^{90} \) \(\mathstrut -\mathstrut 209450940191589584493053736413801309667114864q^{91} \) \(\mathstrut +\mathstrut 31580552157061127996902171853509709970604032q^{92} \) \(\mathstrut -\mathstrut 198656173601061645852049647068499329296299648q^{93} \) \(\mathstrut +\mathstrut 380017168558424107350771392050931198759503872q^{94} \) \(\mathstrut +\mathstrut 11835463674693195649110972576862856536029000q^{95} \) \(\mathstrut +\mathstrut 975255232802529934245987844944349186989490176q^{96} \) \(\mathstrut +\mathstrut 371229894708856356492851438771649466869172902q^{97} \) \(\mathstrut +\mathstrut 19381455993535436564386424979420682870187904q^{98} \) \(\mathstrut -\mathstrut 52499767038004223859624250804879775541363612q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{46}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.46.a.a \(3\) \(12.826\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(3814272\) \(5359866876\) \(-9\!\cdots\!50\) \(-7\!\cdots\!08\) \(+\) \(q+(1271424+\beta _{1})q^{2}+(1786622292+\cdots)q^{3}+\cdots\)