Properties

Label 1.62.a
Level 1
Weight 62
Character orbit a
Rep. character \(\chi_{1}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 62 \)
Character orbit: \([\chi]\) = 1.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{62}(\Gamma_0(1))\).

Total New Old
Modular forms 5 5 0
Cusp forms 4 4 0
Eisenstein series 1 1 0

Trace form

\(4q \) \(\mathstrut +\mathstrut 1146312000q^{2} \) \(\mathstrut -\mathstrut 573723599022000q^{3} \) \(\mathstrut +\mathstrut 4402997675828604928q^{4} \) \(\mathstrut -\mathstrut 524125996020295237800q^{5} \) \(\mathstrut -\mathstrut 810420388530698747434752q^{6} \) \(\mathstrut -\mathstrut 63338569463385158773180000q^{7} \) \(\mathstrut +\mathstrut 9767868387156674079031296000q^{8} \) \(\mathstrut +\mathstrut 116559153778048577840676094452q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 1146312000q^{2} \) \(\mathstrut -\mathstrut 573723599022000q^{3} \) \(\mathstrut +\mathstrut 4402997675828604928q^{4} \) \(\mathstrut -\mathstrut 524125996020295237800q^{5} \) \(\mathstrut -\mathstrut 810420388530698747434752q^{6} \) \(\mathstrut -\mathstrut 63338569463385158773180000q^{7} \) \(\mathstrut +\mathstrut 9767868387156674079031296000q^{8} \) \(\mathstrut +\mathstrut 116559153778048577840676094452q^{9} \) \(\mathstrut -\mathstrut 1483353386285070117088509033600q^{10} \) \(\mathstrut -\mathstrut 41554515064513200044500416014352q^{11} \) \(\mathstrut -\mathstrut 997468469175503713040400254976000q^{12} \) \(\mathstrut +\mathstrut 10764994985103189070396812401291000q^{13} \) \(\mathstrut -\mathstrut 211155135436541225684077605177122304q^{14} \) \(\mathstrut +\mathstrut 115082099805150572294379175169983200q^{15} \) \(\mathstrut +\mathstrut 10904646278227442826771588888892801024q^{16} \) \(\mathstrut -\mathstrut 40906325415811699311242283170389539000q^{17} \) \(\mathstrut +\mathstrut 15755547385947548040677485816834728000q^{18} \) \(\mathstrut -\mathstrut 356159749895948464708913853630763435120q^{19} \) \(\mathstrut -\mathstrut 5071632401696432486275641956774663577600q^{20} \) \(\mathstrut -\mathstrut 5584164717140650613271728795305539583872q^{21} \) \(\mathstrut -\mathstrut 172062995599931314756360229299481569056000q^{22} \) \(\mathstrut -\mathstrut 410968880183827232479513482663937487796000q^{23} \) \(\mathstrut -\mathstrut 6122904790572089676121487755102001729372160q^{24} \) \(\mathstrut -\mathstrut 16739487717977510894946357652146107782722500q^{25} \) \(\mathstrut -\mathstrut 49284147216613914166808777620995485562632832q^{26} \) \(\mathstrut -\mathstrut 128445331744621566171958781429920350730764000q^{27} \) \(\mathstrut -\mathstrut 790757236315065917044952859738895406239744000q^{28} \) \(\mathstrut +\mathstrut 6672429803576117328528976307882755467518520q^{29} \) \(\mathstrut +\mathstrut 957801420237120366977197975859498893217318400q^{30} \) \(\mathstrut +\mathstrut 3262752943509002552517145952336046015034252928q^{31} \) \(\mathstrut +\mathstrut 29552482936847865082009297897367834619543552000q^{32} \) \(\mathstrut +\mathstrut 80589779417942769949681652178013443031895736000q^{33} \) \(\mathstrut +\mathstrut 39802528145537101299701822666373970434557030016q^{34} \) \(\mathstrut +\mathstrut 94932144900835792457443003213138857525722942400q^{35} \) \(\mathstrut -\mathstrut 491545590287100270921289917536068279191068430336q^{36} \) \(\mathstrut -\mathstrut 710312106544219153529408139748985993336062057000q^{37} \) \(\mathstrut -\mathstrut 6572443117826428556368685861295549874330331616000q^{38} \) \(\mathstrut -\mathstrut 5385266212680187341486607570713939645234734498976q^{39} \) \(\mathstrut -\mathstrut 6935278763126032494337494583468084555036360704000q^{40} \) \(\mathstrut +\mathstrut 16359554122032268527799184148245398149035867491368q^{41} \) \(\mathstrut +\mathstrut 150386101138325781804352908808507125636957747456000q^{42} \) \(\mathstrut +\mathstrut 75844732497959094206655920598930086763379517030000q^{43} \) \(\mathstrut +\mathstrut 152692943245212279510621538861388707588508390670336q^{44} \) \(\mathstrut +\mathstrut 60471855189024852796163743559032445559203109252600q^{45} \) \(\mathstrut -\mathstrut 150345409740296355038882940983341438053393810381312q^{46} \) \(\mathstrut -\mathstrut 2164761335188781225334544122222333542985932701416000q^{47} \) \(\mathstrut -\mathstrut 8471840837080202754288377889649147778899824869376000q^{48} \) \(\mathstrut +\mathstrut 1523957834189526415441239854498433329172794287478628q^{49} \) \(\mathstrut -\mathstrut 3735723416225956799610935352239535395426733934920000q^{50} \) \(\mathstrut +\mathstrut 20623083900467721702728328179464369078682764374557088q^{51} \) \(\mathstrut +\mathstrut 34115942043101628674837973043915515701891779834880000q^{52} \) \(\mathstrut +\mathstrut 84459499120263342936174700173047508278523729350943000q^{53} \) \(\mathstrut +\mathstrut 205362219171375312837640062328590989381764073364257280q^{54} \) \(\mathstrut -\mathstrut 18917852463295959783361213875825060571992233753013600q^{55} \) \(\mathstrut -\mathstrut 895534119833025861281009767571957442822737699977297920q^{56} \) \(\mathstrut -\mathstrut 485813603178903589098646017006457442516302171963128000q^{57} \) \(\mathstrut -\mathstrut 429363306259072204179262197105630766591459158948624000q^{58} \) \(\mathstrut -\mathstrut 2147121767784312006347793068275982647255821920255956560q^{59} \) \(\mathstrut +\mathstrut 1658171820897328745993674937960453150336599512561254400q^{60} \) \(\mathstrut +\mathstrut 4291528347018103219994434901020564652244372107292350648q^{61} \) \(\mathstrut +\mathstrut 5191805357629316458585917076609024961942995611849984000q^{62} \) \(\mathstrut +\mathstrut 17756655477174334714938166349329711292289832299011892000q^{63} \) \(\mathstrut +\mathstrut 19881300699476524526504677072626341971094030107078033408q^{64} \) \(\mathstrut -\mathstrut 4054154514265281184405976695522203389642082195785626800q^{65} \) \(\mathstrut -\mathstrut 32579846274793617809975626285379717775321739705823437824q^{66} \) \(\mathstrut -\mathstrut 151638661420806044794238226134660440129857438609787534000q^{67} \) \(\mathstrut -\mathstrut 199797070973791372723379406738475848419062088637699072000q^{68} \) \(\mathstrut -\mathstrut 65270530395832676459014735893839800626266812319535206016q^{69} \) \(\mathstrut +\mathstrut 164781406287311752350371419457017830072394299112015948800q^{70} \) \(\mathstrut +\mathstrut 266771587169907679430401079119295396456876119234283837088q^{71} \) \(\mathstrut +\mathstrut 1006655875418141826396652361065366291089164315936882688000q^{72} \) \(\mathstrut +\mathstrut 436772697766954812846449565799176070423143504803837369000q^{73} \) \(\mathstrut +\mathstrut 2727029156290392414014538532434064649250131670424597597056q^{74} \) \(\mathstrut +\mathstrut 2289194205716179194928001449493608972625299546441763790000q^{75} \) \(\mathstrut -\mathstrut 9182670231472830669367329606616577285345108294701612810240q^{76} \) \(\mathstrut -\mathstrut 6239400117692696801885467207245334802759585122139865360000q^{77} \) \(\mathstrut -\mathstrut 6237267939864197833204910438280167481125291167753285440000q^{78} \) \(\mathstrut -\mathstrut 2171516124052566840962201891051143348431163494068568095680q^{79} \) \(\mathstrut -\mathstrut 8149820448667982873535456900485215194289704343083732172800q^{80} \) \(\mathstrut +\mathstrut 1640511243926006283516650766266777082670562411829996387684q^{81} \) \(\mathstrut +\mathstrut 41751906507711557992784780576518459967807480604061450704000q^{82} \) \(\mathstrut -\mathstrut 19301891587488226996497021336363284746717620338719475718000q^{83} \) \(\mathstrut +\mathstrut 268654655987364118570161060572621663532678550361090391146496q^{84} \) \(\mathstrut +\mathstrut 23823437828438802480990474713115034607148974715085027364400q^{85} \) \(\mathstrut -\mathstrut 71538345696620408289043701603344533132955103857012068207872q^{86} \) \(\mathstrut -\mathstrut 259922121232275661156614167150119002145659028099089961092000q^{87} \) \(\mathstrut -\mathstrut 453611870852754620593515203785357874778152109551115829248000q^{88} \) \(\mathstrut -\mathstrut 606362068644618673179710823370293144593411608656909401212440q^{89} \) \(\mathstrut -\mathstrut 125913175325979481569463842346677014059444686232867490908800q^{90} \) \(\mathstrut -\mathstrut 452168126000372891758634520948160370052422021946362710252352q^{91} \) \(\mathstrut +\mathstrut 1607280224434271875135145612458728092411753130630908891136000q^{92} \) \(\mathstrut -\mathstrut 430218455333355948319021852668117857154414287268428877504000q^{93} \) \(\mathstrut +\mathstrut 6446155892605066539979931910636020289279531063064695408331776q^{94} \) \(\mathstrut +\mathstrut 1105507768048183718212260841102299501129184381013780070972000q^{95} \) \(\mathstrut +\mathstrut 1502030317602264351709698333215472188025674435863914750148608q^{96} \) \(\mathstrut -\mathstrut 8084830239737746227548751167926342536453719541548201116411000q^{97} \) \(\mathstrut +\mathstrut 17015397362965438448003410858883076702895502959466609182344000q^{98} \) \(\mathstrut -\mathstrut 31217771142326421061022583768766679122998622357827944348749776q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{62}^{\mathrm{new}}(\Gamma_0(1))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1.62.a.a \(4\) \(23.566\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(1146312000\) \(-5\!\cdots\!00\) \(-5\!\cdots\!00\) \(-6\!\cdots\!00\) \(+\) \(q+(286578000-\beta _{1})q^{2}+(-143430899755500+\cdots)q^{3}+\cdots\)