Properties

Label 1.46.a
Level 1
Weight 46
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{46}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

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 \(3814272\) \(5359866876\) \(-9\!\cdots\!50\) \(-7\!\cdots\!08\) \(+\) \(q+(1271424+\beta _{1})q^{2}+(1786622292+\cdots)q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3814272 T + 61008476024832 T^{2} - \)\(13\!\cdots\!00\)\( T^{3} + \)\(21\!\cdots\!24\)\( T^{4} - \)\(47\!\cdots\!28\)\( T^{5} + \)\(43\!\cdots\!68\)\( T^{6} \)
$3$ \( 1 - 5359866876 T + \)\(38\!\cdots\!93\)\( T^{2} - \)\(11\!\cdots\!00\)\( T^{3} + \)\(11\!\cdots\!99\)\( T^{4} - \)\(46\!\cdots\!24\)\( T^{5} + \)\(25\!\cdots\!07\)\( T^{6} \)
$5$ \( 1 + 912448458460350 T + \)\(21\!\cdots\!75\)\( T^{2} + \)\(18\!\cdots\!00\)\( T^{3} + \)\(59\!\cdots\!75\)\( T^{4} + \)\(73\!\cdots\!50\)\( T^{5} + \)\(22\!\cdots\!25\)\( T^{6} \)
$7$ \( 1 + 7619710926638056008 T + \)\(15\!\cdots\!57\)\( T^{2} + \)\(41\!\cdots\!00\)\( T^{3} + \)\(16\!\cdots\!99\)\( T^{4} + \)\(87\!\cdots\!92\)\( T^{5} + \)\(12\!\cdots\!43\)\( T^{6} \)
$11$ \( 1 + \)\(29\!\cdots\!44\)\( T + \)\(14\!\cdots\!65\)\( T^{2} + \)\(45\!\cdots\!80\)\( T^{3} + \)\(10\!\cdots\!15\)\( T^{4} + \)\(15\!\cdots\!44\)\( T^{5} + \)\(38\!\cdots\!51\)\( T^{6} \)
$13$ \( 1 + \)\(24\!\cdots\!54\)\( T + \)\(49\!\cdots\!43\)\( T^{2} + \)\(62\!\cdots\!00\)\( T^{3} + \)\(66\!\cdots\!99\)\( T^{4} + \)\(43\!\cdots\!46\)\( T^{5} + \)\(24\!\cdots\!57\)\( T^{6} \)
$17$ \( 1 - \)\(11\!\cdots\!82\)\( T + \)\(51\!\cdots\!07\)\( T^{2} - \)\(76\!\cdots\!00\)\( T^{3} + \)\(12\!\cdots\!99\)\( T^{4} - \)\(64\!\cdots\!18\)\( T^{5} + \)\(12\!\cdots\!93\)\( T^{6} \)
$19$ \( 1 - \)\(13\!\cdots\!80\)\( T + \)\(15\!\cdots\!97\)\( T^{2} - \)\(10\!\cdots\!40\)\( T^{3} + \)\(55\!\cdots\!03\)\( T^{4} - \)\(17\!\cdots\!80\)\( T^{5} + \)\(42\!\cdots\!99\)\( T^{6} \)
$23$ \( 1 + \)\(10\!\cdots\!84\)\( T + \)\(93\!\cdots\!93\)\( T^{2} + \)\(44\!\cdots\!00\)\( T^{3} + \)\(17\!\cdots\!99\)\( T^{4} + \)\(38\!\cdots\!16\)\( T^{5} + \)\(68\!\cdots\!07\)\( T^{6} \)
$29$ \( 1 + \)\(67\!\cdots\!30\)\( T + \)\(10\!\cdots\!47\)\( T^{2} + \)\(83\!\cdots\!40\)\( T^{3} + \)\(65\!\cdots\!03\)\( T^{4} + \)\(27\!\cdots\!30\)\( T^{5} + \)\(26\!\cdots\!49\)\( T^{6} \)
$31$ \( 1 + \)\(43\!\cdots\!44\)\( T + \)\(43\!\cdots\!65\)\( T^{2} + \)\(11\!\cdots\!80\)\( T^{3} + \)\(55\!\cdots\!15\)\( T^{4} + \)\(72\!\cdots\!44\)\( T^{5} + \)\(21\!\cdots\!51\)\( T^{6} \)
$37$ \( 1 + \)\(38\!\cdots\!38\)\( T + \)\(16\!\cdots\!07\)\( T^{2} + \)\(30\!\cdots\!00\)\( T^{3} + \)\(59\!\cdots\!99\)\( T^{4} + \)\(53\!\cdots\!62\)\( T^{5} + \)\(50\!\cdots\!93\)\( T^{6} \)
$41$ \( 1 - \)\(27\!\cdots\!06\)\( T + \)\(12\!\cdots\!15\)\( T^{2} - \)\(20\!\cdots\!20\)\( T^{3} + \)\(46\!\cdots\!15\)\( T^{4} - \)\(38\!\cdots\!06\)\( T^{5} + \)\(53\!\cdots\!01\)\( T^{6} \)
$43$ \( 1 - \)\(12\!\cdots\!56\)\( T + \)\(31\!\cdots\!93\)\( T^{2} - \)\(20\!\cdots\!00\)\( T^{3} + \)\(10\!\cdots\!99\)\( T^{4} - \)\(12\!\cdots\!44\)\( T^{5} + \)\(32\!\cdots\!07\)\( T^{6} \)
$47$ \( 1 + \)\(53\!\cdots\!48\)\( T + \)\(27\!\cdots\!57\)\( T^{2} - \)\(60\!\cdots\!00\)\( T^{3} + \)\(48\!\cdots\!99\)\( T^{4} + \)\(16\!\cdots\!52\)\( T^{5} + \)\(54\!\cdots\!43\)\( T^{6} \)
$53$ \( 1 + \)\(18\!\cdots\!74\)\( T + \)\(22\!\cdots\!43\)\( T^{2} + \)\(16\!\cdots\!00\)\( T^{3} + \)\(86\!\cdots\!99\)\( T^{4} + \)\(28\!\cdots\!26\)\( T^{5} + \)\(59\!\cdots\!57\)\( T^{6} \)
$59$ \( 1 + \)\(35\!\cdots\!60\)\( T + \)\(46\!\cdots\!97\)\( T^{2} - \)\(62\!\cdots\!20\)\( T^{3} + \)\(22\!\cdots\!03\)\( T^{4} + \)\(85\!\cdots\!60\)\( T^{5} + \)\(11\!\cdots\!99\)\( T^{6} \)
$61$ \( 1 + \)\(51\!\cdots\!94\)\( T + \)\(13\!\cdots\!15\)\( T^{2} + \)\(23\!\cdots\!80\)\( T^{3} + \)\(30\!\cdots\!15\)\( T^{4} + \)\(24\!\cdots\!94\)\( T^{5} + \)\(10\!\cdots\!01\)\( T^{6} \)
$67$ \( 1 - \)\(14\!\cdots\!32\)\( T - \)\(71\!\cdots\!43\)\( T^{2} + \)\(17\!\cdots\!00\)\( T^{3} - \)\(10\!\cdots\!01\)\( T^{4} - \)\(31\!\cdots\!68\)\( T^{5} + \)\(33\!\cdots\!43\)\( T^{6} \)
$71$ \( 1 + \)\(12\!\cdots\!44\)\( T + \)\(39\!\cdots\!65\)\( T^{2} + \)\(60\!\cdots\!80\)\( T^{3} + \)\(80\!\cdots\!15\)\( T^{4} + \)\(51\!\cdots\!44\)\( T^{5} + \)\(83\!\cdots\!51\)\( T^{6} \)
$73$ \( 1 - \)\(54\!\cdots\!66\)\( T + \)\(10\!\cdots\!43\)\( T^{2} - \)\(12\!\cdots\!00\)\( T^{3} + \)\(76\!\cdots\!99\)\( T^{4} - \)\(27\!\cdots\!34\)\( T^{5} + \)\(35\!\cdots\!57\)\( T^{6} \)
$79$ \( 1 - \)\(90\!\cdots\!20\)\( T + \)\(66\!\cdots\!97\)\( T^{2} - \)\(49\!\cdots\!60\)\( T^{3} + \)\(16\!\cdots\!03\)\( T^{4} - \)\(55\!\cdots\!20\)\( T^{5} + \)\(15\!\cdots\!99\)\( T^{6} \)
$83$ \( 1 - \)\(14\!\cdots\!36\)\( T + \)\(64\!\cdots\!93\)\( T^{2} - \)\(63\!\cdots\!00\)\( T^{3} + \)\(14\!\cdots\!99\)\( T^{4} - \)\(77\!\cdots\!64\)\( T^{5} + \)\(11\!\cdots\!07\)\( T^{6} \)
$89$ \( 1 + \)\(15\!\cdots\!90\)\( T + \)\(23\!\cdots\!47\)\( T^{2} + \)\(17\!\cdots\!20\)\( T^{3} + \)\(12\!\cdots\!03\)\( T^{4} + \)\(43\!\cdots\!90\)\( T^{5} + \)\(14\!\cdots\!49\)\( T^{6} \)
$97$ \( 1 - \)\(37\!\cdots\!02\)\( T + \)\(66\!\cdots\!07\)\( T^{2} - \)\(16\!\cdots\!00\)\( T^{3} + \)\(16\!\cdots\!99\)\( T^{4} - \)\(23\!\cdots\!98\)\( T^{5} + \)\(16\!\cdots\!93\)\( T^{6} \)
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