LMFDB - Space of Modular Forms of Level 1, Weight 76, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 1 $
Weight:	$ k $	=	$ 76 $
Character orbit:	$[\chi]$	=	1.a (trivial)
Character field:			$\Q$
Newforms:			$ 1 $
Sturm bound:			$6$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{76}(\Gamma_0(1))$.

	Total	New
Modular forms	7	7
Cusp forms	6	6
Eisenstein series	1	1

Trace form

$6q $ $\mathstrut -\mathstrut 57080822040q^{2} $ $\mathstrut -\mathstrut 785092363818710040q^{3} $ $\mathstrut +\mathstrut 172600466200162028593728q^{4} $ $\mathstrut -\mathstrut 38982947396479621874420940q^{5} $ $\mathstrut +\mathstrut 31673308599187435504995050592q^{6} $ $\mathstrut +\mathstrut 1924474634802918779239478643600q^{7} $ $\mathstrut +\mathstrut 4434903997968330342413437320645120q^{8} $ $\mathstrut +\mathstrut 2119498765962992970568250560046009982q^{9} $ $\mathstrut +\mathstrut 133267935677460241037537052811576902960q^{10} $ $\mathstrut -\mathstrut 945659951949983071650740113735111214088q^{11} $ $\mathstrut -\mathstrut 115150003643542480663442829411536163866880q^{12} $ $\mathstrut +\mathstrut 533185179266852519941169625089098069764420q^{13} $ $\mathstrut +\mathstrut 8213946953162263647781694565284746353072576q^{14} $ $\mathstrut -\mathstrut 309603328848013864510094045586663272616092880q^{15} $ $\mathstrut +\mathstrut 2681978005634517266622433394712415602648354816q^{16} $ $\mathstrut +\mathstrut 18261354095776132566172834671579513215483393580q^{17} $ $\mathstrut -\mathstrut 439276854274063146050579040790064492160853960440q^{18} $ $\mathstrut +\mathstrut 1061534856238354155312794852768417904375328867080q^{19} $ $\mathstrut +\mathstrut 9296557595621768320156983882258818695571369489280q^{20} $ $\mathstrut -\mathstrut 100259704699697889376866621361897766152209395224128q^{21} $ $\mathstrut +\mathstrut 153315952874260268106194796405555863940172791589920q^{22} $ $\mathstrut +\mathstrut 1514929449877410771078348320690686508954384916853680q^{23} $ $\mathstrut -\mathstrut 7662424782495949976733296347258884300404709513308160q^{24} $ $\mathstrut +\mathstrut 19310380328261093150952553553121815533899364092239850q^{25} $ $\mathstrut +\mathstrut 117730941166816926498584842564210483616872200198362352q^{26} $ $\mathstrut -\mathstrut 1074213478466937258572560754951503958791056763891563120q^{27} $ $\mathstrut +\mathstrut 1465885017268620651444113586751990931877154821040657920q^{28} $ $\mathstrut +\mathstrut 14718767377678125816030788545177391174717388984245534820q^{29} $ $\mathstrut -\mathstrut 25550285934396345286029563779360588150614380222554150080q^{30} $ $\mathstrut -\mathstrut 41742874787360498453628839393549579933009794702042980288q^{31} $ $\mathstrut +\mathstrut 1174660148719991756036751189163540495635749096221862952960q^{32} $ $\mathstrut +\mathstrut 592070005239220743874129160617285870488467768711527333920q^{33} $ $\mathstrut +\mathstrut 3034358950124956876257603978888653679838045546922892395856q^{34} $ $\mathstrut +\mathstrut 27299672493656883988453292135086250689495956464846953371360q^{35} $ $\mathstrut +\mathstrut 179176299070088941546343921251311713064325363113137876471616q^{36} $ $\mathstrut +\mathstrut 98517772547646219221591850851651469983797181732879949140340q^{37} $ $\mathstrut +\mathstrut 1257660981102762853948269222064665311191946222029530979162080q^{38} $ $\mathstrut +\mathstrut 2481484269951087933260675611242651218102907933795356739592944q^{39} $ $\mathstrut +\mathstrut 8807901623729426290853411185831313455271917763097593104051200q^{40} $ $\mathstrut +\mathstrut 5039211762207387369185984529408567568647239506257650214613212q^{41} $ $\mathstrut +\mathstrut 43775096530001421204709465357678460315555651574798436125415680q^{42} $ $\mathstrut +\mathstrut 27938749238581541451173935836639198120068956697568041153196600q^{43} $ $\mathstrut -\mathstrut 86388814623354110240559749283671522466589238091463431115801344q^{44} $ $\mathstrut -\mathstrut 237966843556414434005003864386125719471571617536701728123349180q^{45} $ $\mathstrut -\mathstrut 824145803870667307795487213022331547039596870954611528203613888q^{46} $ $\mathstrut -\mathstrut 1386854970430427381646742231466788117324292253074354560479038880q^{47} $ $\mathstrut -\mathstrut 8212215903718675701941242530692185525776363042145818555572305920q^{48} $ $\mathstrut -\mathstrut 5707868790800975784856935495088511133239544554833878775910738442q^{49} $ $\mathstrut +\mathstrut 3144970672685230615695776810799603542575044196614572896663392600q^{50} $ $\mathstrut +\mathstrut 283284046705467654069692648207344729396412677737329641196945232q^{51} $ $\mathstrut +\mathstrut 41677832028141179840113326797899392222702339479233001780216150400q^{52} $ $\mathstrut +\mathstrut 64283727174659970247345252518647455744441825702701764187054106260q^{53} $ $\mathstrut +\mathstrut 780320815712097175721587535401535151075152637184894982834238943680q^{54} $ $\mathstrut +\mathstrut 436876078674971654403803167180324983329224614451635548418098895120q^{55} $ $\mathstrut +\mathstrut 289950797286325881623798664040853221823087783432246887785270865920q^{56} $ $\mathstrut -\mathstrut 671954656600624358379440578322093895610678807911638904039760657440q^{57} $ $\mathstrut -\mathstrut 1763005756244374137396902189067511762184157619699352574614137403280q^{58} $ $\mathstrut -\mathstrut 2478360370933764187935912640189307752170553390931716617591182395560q^{59} $ $\mathstrut -\mathstrut 31792921597254948192279089096854272160617709162962021109081069309440q^{60} $ $\mathstrut -\mathstrut 25641115321477658815889269525514418267074652297034046321782023152988q^{61} $ $\mathstrut -\mathstrut 29014701474354643819936101890527484086880802356768235703173807694080q^{62} $ $\mathstrut +\mathstrut 42929132343455570369238205341690645702689225620502517839786884793040q^{63} $ $\mathstrut +\mathstrut 47683232974651133862719671893097862706511055838864188064811716968448q^{64} $ $\mathstrut +\mathstrut 122110621788131890149667214965152432737153070969379698276880591977720q^{65} $ $\mathstrut +\mathstrut 930528105441795930909966787493137282089786427774739900252891166297984q^{66} $ $\mathstrut +\mathstrut 955579073553339181030887342220313909838725364297810737998207107813480q^{67} $ $\mathstrut +\mathstrut 1237210897217068882936524414359446185548686871817993659403939290386560q^{68} $ $\mathstrut -\mathstrut 1408360468152512186955736181867470428051018587723566870538767575903936q^{69} $ $\mathstrut -\mathstrut 3476902593928340346610001926714053112321275314411181267396530677050240q^{70} $ $\mathstrut -\mathstrut 255682319306096297182489045146623979225804710540351927309367569173488q^{71} $ $\mathstrut -\mathstrut 21189962510693790174049281425747631548583047301946833368066212728860160q^{72} $ $\mathstrut -\mathstrut 30605188898291905719532895918028188508004452865621142257485594115042020q^{73} $ $\mathstrut -\mathstrut 24065024027894599201472448362529876891121294631891709256708009194181584q^{74} $ $\mathstrut +\mathstrut 19463431192157531038934013606638975862465120463567077259244690008282200q^{75} $ $\mathstrut +\mathstrut 100020936372377387464010564774983213070641689274186088752725827576144640q^{76} $ $\mathstrut +\mathstrut 158930415774536768880543239288689183540801263714134710336228496440507200q^{77} $ $\mathstrut +\mathstrut 135490258190773913577197940793442636786883342442786889886654637067611200q^{78} $ $\mathstrut +\mathstrut 116627678166642324332643069323234092884951450625988452824960767925148320q^{79} $ $\mathstrut +\mathstrut 1239310052714502333188756625709169306278438274940582996524184215206748160q^{80} $ $\mathstrut +\mathstrut 294279639721966061337542444477716876114885567907972876173645426056517686q^{81} $ $\mathstrut -\mathstrut 2557649813228840791149140948716215474705151452500921688788291587877236080q^{82} $ $\mathstrut -\mathstrut 798780284119889426515570523310162377392459257634002033911814028088739960q^{83} $ $\mathstrut -\mathstrut 9175580553861138859894612698264948459030459925276038063627639364295153664q^{84} $ $\mathstrut -\mathstrut 3615500806340871685633297735534398118961343923835923286123685237305018840q^{85} $ $\mathstrut +\mathstrut 7245194180836090971883743617494948296636529538939897523257528311698092832q^{86} $ $\mathstrut -\mathstrut 14159312341342352586604709816323870081891838395129433788110753788803266960q^{87} $ $\mathstrut -\mathstrut 4827001398586167572057494186308233100206033194553368013345656010632181760q^{88} $ $\mathstrut +\mathstrut 53575610216125238704584826863934604186542249469498220298044079954014547260q^{89} $ $\mathstrut +\mathstrut 85648802068325073636273691125068892379540509730396664184966156591547899120q^{90} $ $\mathstrut +\mathstrut 34502419684367451829908407139028781594042460695428817715772307436403470432q^{91} $ $\mathstrut +\mathstrut 187445224353587479072026786339601818260697439565538078689222489106585838080q^{92} $ $\mathstrut -\mathstrut 166703912520796821824619485532876155501181179490548097775502842243408462080q^{93} $ $\mathstrut -\mathstrut 296189325151987924691405038954735773676385503565643130818482899021002578304q^{94} $ $\mathstrut +\mathstrut 194934959385332686251927514630723902507701573195047654345319995220933314800q^{95} $ $\mathstrut -\mathstrut 892786287645978875167763571227022376777771426534553548077964657447900151808q^{96} $ $\mathstrut -\mathstrut 747928220344118582344222376208028579242743608466383778453296378427532508980q^{97} $ $\mathstrut -\mathstrut 1663265696927109513221859402309517858944410070626232817304447619248634722520q^{98} $ $\mathstrut -\mathstrut 187241780708811231174609640862544518464431146740439798697006075456653933736q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{76}^{\mathrm{new}}(\Gamma_0(1))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1.76.a.a	$6$	$35.623$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-57080822040$	$-7\!\cdots\!40$	$-3\!\cdots\!40$	$19\!\cdots\!00$	$+$	$q+(-9513470340+\beta _{1})q^{2}+\cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 1 \)
Weight:	\( k \)	=	\( 76 \)
Character orbit:	\([\chi]\)	=	1.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Introduction and more

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{76}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1.76.a

Level	1
Weight	76
Character orbit	a
Rep. character	\(\chi_{1}(1,\cdot)\)
Character field	\(\Q\)
Dimension	6
Newforms	1
Sturm bound	6
Trace bound	0

Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1.76.a.a	\(6\)	\(35.623\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-57080822040\)	\(-7\!\cdots\!40\)	\(-3\!\cdots\!40\)	\(19\!\cdots\!00\)	\(+\)	\(q+(-9513470340+\beta _{1})q^{2}+\cdots\)