Properties

Label 1.104.a
Level 1
Weight 104
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 104 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{104}(\Gamma_0(1))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

Trace form

\(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut 5087569706910766050323040q^{3} \) \(\mathstrut +\mathstrut 48324394003700265820897106483264q^{4} \) \(\mathstrut +\mathstrut 551645266991094947988587979858507120q^{5} \) \(\mathstrut +\mathstrut 2626953258123361256046267420263544594336q^{6} \) \(\mathstrut +\mathstrut 41737594138377573148159523392718424208446400q^{7} \) \(\mathstrut +\mathstrut 109882609245772353721829965115065527112449646080q^{8} \) \(\mathstrut +\mathstrut 35934061358184471683999399496530848001601644543016q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4388929556680440q^{2} \) \(\mathstrut +\mathstrut 5087569706910766050323040q^{3} \) \(\mathstrut +\mathstrut 48324394003700265820897106483264q^{4} \) \(\mathstrut +\mathstrut 551645266991094947988587979858507120q^{5} \) \(\mathstrut +\mathstrut 2626953258123361256046267420263544594336q^{6} \) \(\mathstrut +\mathstrut 41737594138377573148159523392718424208446400q^{7} \) \(\mathstrut +\mathstrut 109882609245772353721829965115065527112449646080q^{8} \) \(\mathstrut +\mathstrut 35934061358184471683999399496530848001601644543016q^{9} \) \(\mathstrut +\mathstrut 2027618525260516073181410940373995286751686815077520q^{10} \) \(\mathstrut -\mathstrut 53564255892798621618914292149029865323976089024126944q^{11} \) \(\mathstrut +\mathstrut 25633960574085217446823189913789134273379599963259585280q^{12} \) \(\mathstrut -\mathstrut 1551327849817932010092927923451244764349197489311375245520q^{13} \) \(\mathstrut +\mathstrut 204985531745225680495392627955462650660602632112553429561408q^{14} \) \(\mathstrut -\mathstrut 3020750766469193774466110593818157380300334453782433876013760q^{15} \) \(\mathstrut +\mathstrut 361863449936885119768267973598726020537150452888847981908594688q^{16} \) \(\mathstrut +\mathstrut 2015497649979997361336875976150254045164880842011155416684792720q^{17} \) \(\mathstrut +\mathstrut 267307540106838323861864757930082029915233950378733807409255489240q^{18} \) \(\mathstrut +\mathstrut 1484734834072313889071781871918609444991921518407889999862194156000q^{19} \) \(\mathstrut +\mathstrut 2550001838610112272657033084622870492091806723524425439331785816960q^{20} \) \(\mathstrut -\mathstrut 468651934282513875675935203933822637725944475261560345505782668354304q^{21} \) \(\mathstrut -\mathstrut 137605849219876342207658729678467678698030207344807412231509580517920q^{22} \) \(\mathstrut +\mathstrut 40599619287653938731347770176481184954623812150658724038701540865523520q^{23} \) \(\mathstrut +\mathstrut 417632054269801118353552142462197805319757108882280256182409075047884800q^{24} \) \(\mathstrut -\mathstrut 362937074225983688614876200177837163768974389374609498487470358942710600q^{25} \) \(\mathstrut -\mathstrut 14030741852054819908281579342280387163553452467847954283089945570102881584q^{26} \) \(\mathstrut +\mathstrut 6310451948770981419229340353143176080605163694982014782921106225679184320q^{27} \) \(\mathstrut +\mathstrut 514148330168929069137279753066565726408108706760021137474482330032788078080q^{28} \) \(\mathstrut -\mathstrut 1109314641409183093552976605346965837461990086922169583222454360155329880400q^{29} \) \(\mathstrut -\mathstrut 31780974033428375753830150804412858338763487684738816318474129735272931696960q^{30} \) \(\mathstrut +\mathstrut 104264780455232531257795764608297281101784409237357406959070797687652099233536q^{31} \) \(\mathstrut +\mathstrut 1028908566996694821915427200010950055520054418022728660586770754660435042467840q^{32} \) \(\mathstrut +\mathstrut 1637064370206527961191840416792241672318252830384788267847230786245723880401280q^{33} \) \(\mathstrut -\mathstrut 16880249585595311287790910689090067879202031794055262067512201336945927884230032q^{34} \) \(\mathstrut -\mathstrut 15809814583992711056872904141791269441389432991285782813731594074561867170321280q^{35} \) \(\mathstrut +\mathstrut 805787623574605247165419461734624389987695467909486995221520106404473098849425728q^{36} \) \(\mathstrut -\mathstrut 92541276402281504667713648425023541514489587998355774759921151431265396409265040q^{37} \) \(\mathstrut +\mathstrut 1971300306790799032342240078744393153702898113403645290763243656535920191023423520q^{38} \) \(\mathstrut -\mathstrut 7885389189078955664633112105466856010714545616525346076007201630144160874672246208q^{39} \) \(\mathstrut +\mathstrut 1977015288844745924714331362379506784318231603612597717318543376316436008269440000q^{40} \) \(\mathstrut +\mathstrut 222749082810191111691395557742339640725571297200098840306597511963716166910016506576q^{41} \) \(\mathstrut -\mathstrut 1883267638769361387897797057480679095562739407538640601371566884432999969422842010880q^{42} \) \(\mathstrut +\mathstrut 968895197607192930930940008787782675398644318852140770090896736295885033488529690400q^{43} \) \(\mathstrut +\mathstrut 2615800371528018307641663183711908967442008589707371423475870586505299691562914926848q^{44} \) \(\mathstrut -\mathstrut 1473010112873063959626609346390652156643077000013339776241472977560123315435112983760q^{45} \) \(\mathstrut +\mathstrut 27446065195956198075877779014773406391109527885085904763819008268953431741208364616896q^{46} \) \(\mathstrut -\mathstrut 293609653174290525998217973440321639247924396408373610899942779596119844480753010677120q^{47} \) \(\mathstrut +\mathstrut 1240474483651634936656271628196732975278107731060035918088958893365811804822813860741120q^{48} \) \(\mathstrut +\mathstrut 2668551616424529602044449137134709537764999196283756605526691963266904852724306068111944q^{49} \) \(\mathstrut -\mathstrut 6521555021853481798089331632691717210870069276041958186139599024744619050092391455132600q^{50} \) \(\mathstrut -\mathstrut 20813334460690950021193410586099062172982223916797529091846346968717683910092635969470784q^{51} \) \(\mathstrut -\mathstrut 36075131888471074369144062637736452287512569193963836276062247375366142706627591324022400q^{52} \) \(\mathstrut +\mathstrut 161574805302535676592212552212935130219348465152378468526413124882553154054403888166112240q^{53} \) \(\mathstrut +\mathstrut 244996591061285005233721911255171344371445084231598513861031145908120404974069967807566400q^{54} \) \(\mathstrut -\mathstrut 607939909864004614075356036982415128356301156312798815333086681706442442074797191568452160q^{55} \) \(\mathstrut -\mathstrut 503347948801547505295544537202800039798463622449253526436143518261972796907682627548672000q^{56} \) \(\mathstrut +\mathstrut 5585281202236608576148075500959180617113370740733374350303663601038337658261844358331674240q^{57} \) \(\mathstrut +\mathstrut 10803107862759337782251611301310445432173113486135052277293695910012872510635542918433350480q^{58} \) \(\mathstrut -\mathstrut 3763669177454952719015429893224775020266577352512033436736083012099637155611183545807925600q^{59} \) \(\mathstrut -\mathstrut 44516663894047516283340986041100025029890327265561963837781098524475428602375001706220910080q^{60} \) \(\mathstrut +\mathstrut 56147145392217940296237629782250660517556168142847888898434987753570576599200638389784423856q^{61} \) \(\mathstrut +\mathstrut 708807506014393204305112275358657132745269481108345030482782405369277364762268787441349556480q^{62} \) \(\mathstrut +\mathstrut 1004547917742295582189356352643083605257294414907733584799000902948644764606451215157969453760q^{63} \) \(\mathstrut +\mathstrut 2689955130199770090919426143081142657167991663226807770013236363849718691785612797260291375104q^{64} \) \(\mathstrut +\mathstrut 5124254892052438764657504605348539922002660919805937289990918847816257298286298313919564321440q^{65} \) \(\mathstrut +\mathstrut 36460770617845857205288107920138564493995889702559578221696109246179691643034860902124792436352q^{66} \) \(\mathstrut +\mathstrut 36212058392130762275437269862682052845105568281986303679248701513796303582516933489238204852320q^{67} \) \(\mathstrut +\mathstrut 121871257184262948410168536656451503789769474779037040449473211419440774288140532505483576282240q^{68} \) \(\mathstrut +\mathstrut 146171714897241059447510875608282423246804848799861315408644138710655320106224092813159842449152q^{69} \) \(\mathstrut +\mathstrut 853756690279911250368037438486434151435346605497824981233696852732671552949658306872737406389120q^{70} \) \(\mathstrut +\mathstrut 1323027110921369091114059758958942708535901440060160919331826835683096477433051757156908929999296q^{71} \) \(\mathstrut +\mathstrut 5635474260733453081095589332277842775365114507654390044914919885310203213431471309882290635036160q^{72} \) \(\mathstrut +\mathstrut 4434337224305117877569754735641925591340191550850949206294860286939824237219014387268913705824720q^{73} \) \(\mathstrut +\mathstrut 9446978778046296456470116730008064896416484139132353834625710442657435714245141545863045630195088q^{74} \) \(\mathstrut +\mathstrut 15788198796594475882673542236654839411090926672421130688549340631916075230881024844909417441328800q^{75} \) \(\mathstrut +\mathstrut 62208878575567502646775884731743768059494074065603793769837837917746101674437608641395557819334400q^{76} \) \(\mathstrut +\mathstrut 37781769005935846521801726968449743374817416956894448777845288067504206491843901930831867790380800q^{77} \) \(\mathstrut +\mathstrut 44019466816742377243458217012569984532155201470078975456308994008831948835905199650013699349604800q^{78} \) \(\mathstrut +\mathstrut 24360542002769992615028834274408332054107188048024574794369918904382062971902552671267968844374400q^{79} \) \(\mathstrut -\mathstrut 257406550547438596244863901420403525688280266364441018588431059738298545930906704910071981299015680q^{80} \) \(\mathstrut -\mathstrut 319858452590968976040706219061802261896767071034600475754637194160339936835204759950912194010523832q^{81} \) \(\mathstrut -\mathstrut 347037715568344180193612732627815416282275947315627995720995526007231252178377268346955612809946320q^{82} \) \(\mathstrut -\mathstrut 2589709199921534719789158381824365674651513931126861560377010891589296789100538920269990341311172640q^{83} \) \(\mathstrut -\mathstrut 14763276600099218032093350675578467421653757870459793949112274722608304409453274353718894336536287232q^{84} \) \(\mathstrut -\mathstrut 7750041700239420480976421024168094692666091522883832659906501732615678081854865932331016250083918880q^{85} \) \(\mathstrut -\mathstrut 22862474248159310408090160685058395474537452344937345785285404938278205476818797847965682857887379744q^{86} \) \(\mathstrut -\mathstrut 19667171614563900919678037177279936924594588506587176946944336641584005321373812755132416018759906240q^{87} \) \(\mathstrut -\mathstrut 40280517105348128384004030315972727789809528309384337508840799111515821927415232196104998546661181440q^{88} \) \(\mathstrut -\mathstrut 2411931583959929374872883405418443793306523554844108736778614462710442635343758894445178420208577200q^{89} \) \(\mathstrut +\mathstrut 19218417888800936875567136220118837811145582599884634713838228828686741391845969008376636752235577040q^{90} \) \(\mathstrut +\mathstrut 157061027064080129827172588737919758324770125960416982485587688356910129161874310994817267624768962176q^{91} \) \(\mathstrut +\mathstrut 773615141308510753640652909662430286328720511338068191045295874258285130068299519150171249463376222720q^{92} \) \(\mathstrut +\mathstrut 1017145077013570534640298063884056653140131362969292242328097944460668594729564068877620396903861703680q^{93} \) \(\mathstrut +\mathstrut 727087863890952033548300791290895488242032063484702253117314469808013304697569232190083038540113931648q^{94} \) \(\mathstrut +\mathstrut 2743732154506646909406097298325321408379587730896118185195801036752841998424162414172669753574660712000q^{95} \) \(\mathstrut +\mathstrut 8873312662336745259606299368794125872185792644230053366160730387846004935345208576954549405340151709696q^{96} \) \(\mathstrut +\mathstrut 5002945503247003905009597326381275147828980571278924405638622881444475469921369111184405290832776414480q^{97} \) \(\mathstrut +\mathstrut 8807510378044686174684586237206775917067603624837914322579837506936931417303594998092206302439262913720q^{98} \) \(\mathstrut -\mathstrut 7247372384990122262319746951941725843983906615680409319965154257589720777414294443683699540960522497888q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{104}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.104.a.a \(8\) \(67.184\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(43\!\cdots\!40\) \(50\!\cdots\!40\) \(55\!\cdots\!20\) \(41\!\cdots\!00\) \(+\) \(q+(548616194585055-\beta _{1})q^{2}+\cdots\)