Properties

Label 1.120.a
Level 1
Weight 120
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 10
Newforms 1
Sturm bound 10
Trace bound 0

Related objects

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 120 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{120}(\Gamma_0(1))\).

Total New Old
Modular forms 11 11 0
Cusp forms 10 10 0
Eisenstein series 1 1 0

Trace form

\(10q \) \(\mathstrut +\mathstrut 919932722605769400q^{2} \) \(\mathstrut -\mathstrut 9570159827289248935296702600q^{3} \) \(\mathstrut +\mathstrut 4272705896834573968338259309906185280q^{4} \) \(\mathstrut +\mathstrut 606257200226243383006472566047160160843340q^{5} \) \(\mathstrut +\mathstrut 36401504491894467383240980519952999483223273120q^{6} \) \(\mathstrut -\mathstrut 219254218938377593670425814743273520801802467026000q^{7} \) \(\mathstrut -\mathstrut 565565131741559483416651174475719665908207742245491200q^{8} \) \(\mathstrut +\mathstrut 1834851904582599922503319964983981808160026773815306152370q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 919932722605769400q^{2} \) \(\mathstrut -\mathstrut 9570159827289248935296702600q^{3} \) \(\mathstrut +\mathstrut 4272705896834573968338259309906185280q^{4} \) \(\mathstrut +\mathstrut 606257200226243383006472566047160160843340q^{5} \) \(\mathstrut +\mathstrut 36401504491894467383240980519952999483223273120q^{6} \) \(\mathstrut -\mathstrut 219254218938377593670425814743273520801802467026000q^{7} \) \(\mathstrut -\mathstrut 565565131741559483416651174475719665908207742245491200q^{8} \) \(\mathstrut +\mathstrut 1834851904582599922503319964983981808160026773815306152370q^{9} \) \(\mathstrut +\mathstrut 634986125367587740207204302796387131018009187401381869153040q^{10} \) \(\mathstrut +\mathstrut 101699246725606790738835774661895063480820812124313881877201320q^{11} \) \(\mathstrut -\mathstrut 38454913569966405167762742595438498566456999771452096076177235200q^{12} \) \(\mathstrut -\mathstrut 1185748520257577664060559883259066024596136377436810629686687725700q^{13} \) \(\mathstrut +\mathstrut 128663533898726556350640086194927332426384167007882730622864072285760q^{14} \) \(\mathstrut -\mathstrut 3710554087524006716347381761626904165187860707894445603427280739742320q^{15} \) \(\mathstrut +\mathstrut 1692157270872518872969972729913243365739971167225638932987297451499458560q^{16} \) \(\mathstrut -\mathstrut 7864283005617688192060113380368906686779951730371226323040594773109948300q^{17} \) \(\mathstrut +\mathstrut 332729677344108131883156941184784577100879720076210912205274121852966805400q^{18} \) \(\mathstrut +\mathstrut 6933132543714084280010692900040098202807958189097871055544810749569091843800q^{19} \) \(\mathstrut +\mathstrut 739362437091413007058366615825358922208924736756157332674630660292607013864320q^{20} \) \(\mathstrut +\mathstrut 2956525867496139343216584028476962325502089413634709218759412375063065769235520q^{21} \) \(\mathstrut +\mathstrut 182048505569729359245793025478209587997846812992510021821256296609773333925464800q^{22} \) \(\mathstrut +\mathstrut 2899273707160329485617593679008001931087825074180318868634550223688404754013405200q^{23} \) \(\mathstrut +\mathstrut 114076958190963694629504891381029963295654961523414627262670720636843992879159552000q^{24} \) \(\mathstrut +\mathstrut 438494787182106380867327117170026697103640781467523702437104047242833362602352949350q^{25} \) \(\mathstrut -\mathstrut 318317418521249562365279268571874153839124425225189223040103737098442975265906223280q^{26} \) \(\mathstrut -\mathstrut 45551493493769742679374192788006036083495765633221136999776547459453349750382686446800q^{27} \) \(\mathstrut -\mathstrut 523381565894005037423609946706950604481078110602387257868273228698395911628601559155200q^{28} \) \(\mathstrut -\mathstrut 239780648672002576188201702569667845017734503354477933365275721637750281457865124433700q^{29} \) \(\mathstrut +\mathstrut 21029395143482710334699445468847496946126462842956505426185423480948664554653809442982080q^{30} \) \(\mathstrut +\mathstrut 160165221449158413670086721746271710279050125440150480736499480204572300135092293246793920q^{31} \) \(\mathstrut -\mathstrut 834373398020641818369077524061840548626893881879494325415144208186283168678479622990233600q^{32} \) \(\mathstrut -\mathstrut 3570238663181267586336948085267071808900587562867500514533738739767476967040829429822599200q^{33} \) \(\mathstrut -\mathstrut 41095955432266996557490146601397116658486035720992194797885692480580962506776105495084173840q^{34} \) \(\mathstrut +\mathstrut 138699704976096510485603716990768616767579130103693747880984703716174722976398003170335643040q^{35} \) \(\mathstrut +\mathstrut 1968770682959423831661461799770758836110419126467351452806841613209828415998369150047869168960q^{36} \) \(\mathstrut -\mathstrut 2929977505416183984446606444699920153402867583929450347729318630774282158879219717208971398900q^{37} \) \(\mathstrut -\mathstrut 34132539768785031258064307777998769213197932649565990492157910428905434754702082210597346456800q^{38} \) \(\mathstrut -\mathstrut 37083836176586549326655714409651173972060300017562592944355756464743632231154290665689117350960q^{39} \) \(\mathstrut +\mathstrut 671451534852984850954224825661781753416230993956537124458730875650510059526361261848342923494400q^{40} \) \(\mathstrut +\mathstrut 2514540111291426044482406571860470483406800557710096621771586537326874081984886304684316806834820q^{41} \) \(\mathstrut -\mathstrut 15273274580038512441282769157227926832173790524876405090470612324607958771986447522111977427436800q^{42} \) \(\mathstrut +\mathstrut 3044753550753493053954517812078986490614702618943897995955026804229546439117864461911484146129000q^{43} \) \(\mathstrut -\mathstrut 12194938044986814191839006674776852072893778556175391506781528253940392493592913843485049137975040q^{44} \) \(\mathstrut +\mathstrut 986746799250062956400338006861900986362523619062838880021292887355485855896798596485569080571667580q^{45} \) \(\mathstrut +\mathstrut 752141612087076748912715482380878319001154104492332189173260174861749530869824058097798503110563520q^{46} \) \(\mathstrut -\mathstrut 1918977170076493454170487365406413018340521940535245265635752086808026838196958796824029488596607200q^{47} \) \(\mathstrut -\mathstrut 9413963382571179425636093740415075791073794954566518162212892225259707570459169592567092964578508800q^{48} \) \(\mathstrut +\mathstrut 4424167233212972548308367231382645770920683128881486958515725055988725408868499618515518765011399130q^{49} \) \(\mathstrut +\mathstrut 680722065409115183760100309976569125874165206805654527502038796615083137012712040535401772639602878600q^{50} \) \(\mathstrut -\mathstrut 32319807059595921198119329763639094466370593528876750378364913074838896902840034535481214151885659280q^{51} \) \(\mathstrut -\mathstrut 3672350508615918706988315428535798947878272949374804570220967811956449680004938673562235859140924944000q^{52} \) \(\mathstrut -\mathstrut 2009211479238083119390289905543378382308797873461290277025114374748986032309712284340399015223172958100q^{53} \) \(\mathstrut -\mathstrut 1931801935997371383558162239941092584008314189522805286105797190362500280610458221586931216805738379200q^{54} \) \(\mathstrut +\mathstrut 30511878931073238316415921138278986771644957150459948535911136025774807284294416560913953468660882079280q^{55} \) \(\mathstrut +\mathstrut 126877575660686062164799530657771058499408094328546461202608068856064827832632677097022676050516125388800q^{56} \) \(\mathstrut -\mathstrut 1412245636613402987583566403928499689907673096626013381053749242060772374057239140716128737047059987589600q^{57} \) \(\mathstrut -\mathstrut 136877557224662485454400622855348052940229394353948623607073498889520831920878560332024651715699006897200q^{58} \) \(\mathstrut +\mathstrut 3299933671312970318014224510035438974811878541147756441623760703525598387045261537239059812342521105337800q^{59} \) \(\mathstrut +\mathstrut 21522094490079259713051153429507985158270932148578747769685503036840800025279058274203907556876957730736640q^{60} \) \(\mathstrut +\mathstrut 4837190174129518173385919119672257037555828391936321041643076409836299786530753347575068109568740623595420q^{61} \) \(\mathstrut -\mathstrut 160819201153827870914932578626796393716485319064275718134936059959659604110154771581583794810946018351763200q^{62} \) \(\mathstrut -\mathstrut 29983538095598409492955452543692543839392503094995599971655215910869017565718274766970279553480154472448400q^{63} \) \(\mathstrut +\mathstrut 1211010735266408368721880715435373923494644777241361683572485488080139913559735067537574947639643472539156480q^{64} \) \(\mathstrut +\mathstrut 275596405736800076158618605370878142954922604093367429122958466182625164052330625944843847143685944773387080q^{65} \) \(\mathstrut -\mathstrut 4571556792821411386452986160291211039829949386539474994568046789054354433826530257625242189399890177231308160q^{66} \) \(\mathstrut -\mathstrut 14492255044540068397146202787177666038978329738091966816085948596075196182415583867767491778681013197600129800q^{67} \) \(\mathstrut +\mathstrut 11412020923423724971791403006719373171687704529451822317715709895446884725238988347133907742324217053213750400q^{68} \) \(\mathstrut +\mathstrut 26214069579412214259271827314973627996718651539417118198340276923109493510587408283690746644729049025547573440q^{69} \) \(\mathstrut +\mathstrut 123614110386251874656201195782002919137175900573453806468611285513805590311860970064321111121804039130548666240q^{70} \) \(\mathstrut +\mathstrut 167986438720991202535175844535056202103467058420138032407837057205213862880922938218281473241336848029824726320q^{71} \) \(\mathstrut -\mathstrut 1214027676200915397665818515850699616086911975452482717359179924343053006357499126921626784766543068325763750400q^{72} \) \(\mathstrut +\mathstrut 1233949202586186335303917316898506861995019601998317675708778649302958930766175545348120938476925924328720549700q^{73} \) \(\mathstrut +\mathstrut 543442580799452155829153254268968536321414860958435747186750896729081968075855332008879736531095204288140166160q^{74} \) \(\mathstrut +\mathstrut 5400719330138615967684042552542859592218848409512888981139070352575924621197393023272032307312948409698674976200q^{75} \) \(\mathstrut -\mathstrut 1947681364249266128008278515237592495027779127950973160394084152671569960150463509448195360313803381416385798400q^{76} \) \(\mathstrut -\mathstrut 16683659822909228960950374914003452078135467020374567292986163653878590289822431170045744715362904216698143432000q^{77} \) \(\mathstrut -\mathstrut 89072355889618061913236422961170201709148241333748665798116496667029121445925030388457750939459839052612461352000q^{78} \) \(\mathstrut +\mathstrut 157508184913938702697109095010204757626061191800741192129723961816007368467430024268154560701305365480554014277600q^{79} \) \(\mathstrut +\mathstrut 717738694171956562725550070775822043413971269412641242062469275441459076310474017521997792969717993348643119882240q^{80} \) \(\mathstrut +\mathstrut 685377716933108811002635995136680562114143448286890027079208804131082571599201228615213084084612556502713839645210q^{81} \) \(\mathstrut -\mathstrut 81231248886594142360412634887129249452756426241963903730935732338634849662649563859028187215008243901359954917200q^{82} \) \(\mathstrut -\mathstrut 1206868514083202720232704577481117752069506004611956039833793542006699255448280107179126221895523030200058209215400q^{83} \) \(\mathstrut +\mathstrut 14126467866143646431573189552438805296686170961752631529359503040694891931287469221548265077514565520405417102632960q^{84} \) \(\mathstrut +\mathstrut 14020561046474179165946028061965977084369651578728211422336420822319994099510809728088754276111040551899070188910040q^{85} \) \(\mathstrut +\mathstrut 66344225309049944615999973318384392854563837752586977497952258411148013864305631982269419370065960537615017456509920q^{86} \) \(\mathstrut +\mathstrut 42211584651436829046971577208962080119193312751750182233070614864898561469568330009329188990317590094811388534891600q^{87} \) \(\mathstrut +\mathstrut 137328180658233895389586672135196831011178161508672801678233870639146210732539922411594570311726409571327613009049600q^{88} \) \(\mathstrut +\mathstrut 419216508652667251481624162222063794117236701682826141556295380005381004122845062519830860537035472363408866073492900q^{89} \) \(\mathstrut +\mathstrut 1960186172906516738137093246273215583954033628616907194913300477767254569348788187788783980642894284377261444786246480q^{90} \) \(\mathstrut +\mathstrut 2117961972511642186570565583354551994813643511649789410299502995928572494930166279095010158484303424328709161629477920q^{91} \) \(\mathstrut +\mathstrut 7643877538850487094208225981990239274508968935126003265201353928208290718282344963218624186914954600357688007403379200q^{92} \) \(\mathstrut +\mathstrut 4145125513717754925972762047991995413704692770483070724240680311937909051760759841371162072158739134468687943292012800q^{93} \) \(\mathstrut +\mathstrut 18905124986143721068825997229954909071618392026686975237140598903838373039063178431388647564880138863772474056628453760q^{94} \) \(\mathstrut +\mathstrut 24103470106743892259389808018645838698305984759500570316746447180409251673952803385627315633849766600459698430524475600q^{95} \) \(\mathstrut +\mathstrut 145148996310095551220695234868863345553364456500073995562810300405246452541716926663419327678590987234751701850742456320q^{96} \) \(\mathstrut +\mathstrut 107546374851676082038883438148873453454117013661188535495956674032604491178648329876169635437402337745265739065665481300q^{97} \) \(\mathstrut +\mathstrut 174218963757049243228974277723290518756443094205275131612770946890670481716398629353987179661401811795718431811507182200q^{98} \) \(\mathstrut +\mathstrut 323496911757957747789115751830719500571150759171653307778212471313230140211264055128690873120449943627772784580871392840q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{120}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.120.a.a \(10\) \(89.678\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(91\!\cdots\!00\) \(-9\!\cdots\!00\) \(60\!\cdots\!40\) \(-2\!\cdots\!00\) \(+\) \(q+(91993272260576940-\beta _{1})q^{2}+\cdots\)