Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 62 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{62}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 1146312000 T + 3067202781185085440 T^{2} - \)\(53\!\cdots\!00\)\( T^{3} + \)\(70\!\cdots\!08\)\( T^{4} - \)\(12\!\cdots\!00\)\( T^{5} + \)\(16\!\cdots\!60\)\( T^{6} - \)\(14\!\cdots\!00\)\( T^{7} + \)\(28\!\cdots\!16\)\( T^{8} \)
$3$ \( 1 + 573723599022000 T + \)\(36\!\cdots\!80\)\( T^{2} + \)\(16\!\cdots\!00\)\( T^{3} + \)\(69\!\cdots\!18\)\( T^{4} + \)\(20\!\cdots\!00\)\( T^{5} + \)\(58\!\cdots\!20\)\( T^{6} + \)\(11\!\cdots\!00\)\( T^{7} + \)\(26\!\cdots\!81\)\( T^{8} \)
$5$ \( 1 + \)\(52\!\cdots\!00\)\( T + \)\(17\!\cdots\!00\)\( T^{2} + \)\(67\!\cdots\!00\)\( T^{3} + \)\(11\!\cdots\!50\)\( T^{4} + \)\(29\!\cdots\!00\)\( T^{5} + \)\(32\!\cdots\!00\)\( T^{6} + \)\(42\!\cdots\!00\)\( T^{7} + \)\(35\!\cdots\!25\)\( T^{8} \)
$7$ \( 1 + \)\(63\!\cdots\!00\)\( T + \)\(83\!\cdots\!00\)\( T^{2} + \)\(47\!\cdots\!00\)\( T^{3} + \)\(38\!\cdots\!98\)\( T^{4} + \)\(17\!\cdots\!00\)\( T^{5} + \)\(10\!\cdots\!00\)\( T^{6} + \)\(28\!\cdots\!00\)\( T^{7} + \)\(15\!\cdots\!01\)\( T^{8} \)
$11$ \( 1 + \)\(41\!\cdots\!52\)\( T + \)\(70\!\cdots\!08\)\( T^{2} + \)\(24\!\cdots\!04\)\( T^{3} + \)\(24\!\cdots\!70\)\( T^{4} + \)\(81\!\cdots\!44\)\( T^{5} + \)\(78\!\cdots\!68\)\( T^{6} + \)\(15\!\cdots\!12\)\( T^{7} + \)\(12\!\cdots\!41\)\( T^{8} \)
$13$ \( 1 - \)\(10\!\cdots\!00\)\( T + \)\(17\!\cdots\!60\)\( T^{2} - \)\(12\!\cdots\!00\)\( T^{3} + \)\(14\!\cdots\!38\)\( T^{4} - \)\(10\!\cdots\!00\)\( T^{5} + \)\(13\!\cdots\!40\)\( T^{6} - \)\(76\!\cdots\!00\)\( T^{7} + \)\(63\!\cdots\!61\)\( T^{8} \)
$17$ \( 1 + \)\(40\!\cdots\!00\)\( T + \)\(40\!\cdots\!20\)\( T^{2} + \)\(10\!\cdots\!00\)\( T^{3} + \)\(63\!\cdots\!78\)\( T^{4} + \)\(11\!\cdots\!00\)\( T^{5} + \)\(52\!\cdots\!80\)\( T^{6} + \)\(60\!\cdots\!00\)\( T^{7} + \)\(16\!\cdots\!21\)\( T^{8} \)
$19$ \( 1 + \)\(35\!\cdots\!20\)\( T + \)\(16\!\cdots\!76\)\( T^{2} + \)\(29\!\cdots\!40\)\( T^{3} + \)\(19\!\cdots\!66\)\( T^{4} + \)\(29\!\cdots\!60\)\( T^{5} + \)\(16\!\cdots\!36\)\( T^{6} + \)\(36\!\cdots\!80\)\( T^{7} + \)\(10\!\cdots\!21\)\( T^{8} \)
$23$ \( 1 + \)\(41\!\cdots\!00\)\( T + \)\(43\!\cdots\!40\)\( T^{2} + \)\(13\!\cdots\!00\)\( T^{3} + \)\(73\!\cdots\!58\)\( T^{4} + \)\(15\!\cdots\!00\)\( T^{5} + \)\(58\!\cdots\!60\)\( T^{6} + \)\(64\!\cdots\!00\)\( T^{7} + \)\(18\!\cdots\!41\)\( T^{8} \)
$29$ \( 1 - \)\(66\!\cdots\!20\)\( T + \)\(43\!\cdots\!16\)\( T^{2} + \)\(46\!\cdots\!60\)\( T^{3} + \)\(85\!\cdots\!46\)\( T^{4} + \)\(74\!\cdots\!40\)\( T^{5} + \)\(11\!\cdots\!56\)\( T^{6} - \)\(27\!\cdots\!80\)\( T^{7} + \)\(66\!\cdots\!81\)\( T^{8} \)
$31$ \( 1 - \)\(32\!\cdots\!28\)\( T + \)\(28\!\cdots\!68\)\( T^{2} - \)\(75\!\cdots\!76\)\( T^{3} + \)\(38\!\cdots\!70\)\( T^{4} - \)\(70\!\cdots\!56\)\( T^{5} + \)\(25\!\cdots\!48\)\( T^{6} - \)\(27\!\cdots\!48\)\( T^{7} + \)\(78\!\cdots\!21\)\( T^{8} \)
$37$ \( 1 + \)\(71\!\cdots\!00\)\( T + \)\(98\!\cdots\!60\)\( T^{2} + \)\(68\!\cdots\!00\)\( T^{3} + \)\(69\!\cdots\!38\)\( T^{4} + \)\(31\!\cdots\!00\)\( T^{5} + \)\(20\!\cdots\!40\)\( T^{6} + \)\(67\!\cdots\!00\)\( T^{7} + \)\(43\!\cdots\!61\)\( T^{8} \)
$41$ \( 1 - \)\(16\!\cdots\!68\)\( T + \)\(80\!\cdots\!48\)\( T^{2} - \)\(85\!\cdots\!16\)\( T^{3} + \)\(26\!\cdots\!70\)\( T^{4} - \)\(20\!\cdots\!56\)\( T^{5} + \)\(46\!\cdots\!88\)\( T^{6} - \)\(22\!\cdots\!28\)\( T^{7} + \)\(33\!\cdots\!61\)\( T^{8} \)
$43$ \( 1 - \)\(75\!\cdots\!00\)\( T + \)\(13\!\cdots\!00\)\( T^{2} - \)\(79\!\cdots\!00\)\( T^{3} + \)\(84\!\cdots\!98\)\( T^{4} - \)\(34\!\cdots\!00\)\( T^{5} + \)\(25\!\cdots\!00\)\( T^{6} - \)\(63\!\cdots\!00\)\( T^{7} + \)\(36\!\cdots\!01\)\( T^{8} \)
$47$ \( 1 + \)\(21\!\cdots\!00\)\( T + \)\(36\!\cdots\!80\)\( T^{2} + \)\(46\!\cdots\!00\)\( T^{3} + \)\(54\!\cdots\!18\)\( T^{4} + \)\(45\!\cdots\!00\)\( T^{5} + \)\(36\!\cdots\!20\)\( T^{6} + \)\(21\!\cdots\!00\)\( T^{7} + \)\(98\!\cdots\!81\)\( T^{8} \)
$53$ \( 1 - \)\(84\!\cdots\!00\)\( T + \)\(55\!\cdots\!80\)\( T^{2} - \)\(20\!\cdots\!00\)\( T^{3} + \)\(89\!\cdots\!18\)\( T^{4} - \)\(31\!\cdots\!00\)\( T^{5} + \)\(12\!\cdots\!20\)\( T^{6} - \)\(29\!\cdots\!00\)\( T^{7} + \)\(52\!\cdots\!81\)\( T^{8} \)
$59$ \( 1 + \)\(21\!\cdots\!60\)\( T + \)\(37\!\cdots\!36\)\( T^{2} + \)\(50\!\cdots\!20\)\( T^{3} + \)\(62\!\cdots\!86\)\( T^{4} + \)\(53\!\cdots\!80\)\( T^{5} + \)\(41\!\cdots\!16\)\( T^{6} + \)\(24\!\cdots\!40\)\( T^{7} + \)\(12\!\cdots\!61\)\( T^{8} \)
$61$ \( 1 - \)\(42\!\cdots\!48\)\( T + \)\(31\!\cdots\!08\)\( T^{2} - \)\(10\!\cdots\!96\)\( T^{3} + \)\(37\!\cdots\!70\)\( T^{4} - \)\(81\!\cdots\!56\)\( T^{5} + \)\(20\!\cdots\!68\)\( T^{6} - \)\(22\!\cdots\!88\)\( T^{7} + \)\(41\!\cdots\!41\)\( T^{8} \)
$67$ \( 1 + \)\(15\!\cdots\!00\)\( T + \)\(14\!\cdots\!20\)\( T^{2} + \)\(10\!\cdots\!00\)\( T^{3} + \)\(56\!\cdots\!78\)\( T^{4} + \)\(24\!\cdots\!00\)\( T^{5} + \)\(89\!\cdots\!80\)\( T^{6} + \)\(22\!\cdots\!00\)\( T^{7} + \)\(36\!\cdots\!21\)\( T^{8} \)
$71$ \( 1 - \)\(26\!\cdots\!88\)\( T + \)\(15\!\cdots\!88\)\( T^{2} + \)\(22\!\cdots\!64\)\( T^{3} + \)\(64\!\cdots\!70\)\( T^{4} + \)\(18\!\cdots\!44\)\( T^{5} + \)\(10\!\cdots\!08\)\( T^{6} - \)\(16\!\cdots\!68\)\( T^{7} + \)\(50\!\cdots\!81\)\( T^{8} \)
$73$ \( 1 - \)\(43\!\cdots\!00\)\( T + \)\(13\!\cdots\!40\)\( T^{2} - \)\(45\!\cdots\!00\)\( T^{3} + \)\(84\!\cdots\!58\)\( T^{4} - \)\(20\!\cdots\!00\)\( T^{5} + \)\(28\!\cdots\!60\)\( T^{6} - \)\(42\!\cdots\!00\)\( T^{7} + \)\(44\!\cdots\!41\)\( T^{8} \)
$79$ \( 1 + \)\(21\!\cdots\!80\)\( T + \)\(11\!\cdots\!16\)\( T^{2} - \)\(36\!\cdots\!40\)\( T^{3} + \)\(56\!\cdots\!46\)\( T^{4} - \)\(20\!\cdots\!60\)\( T^{5} + \)\(38\!\cdots\!56\)\( T^{6} + \)\(40\!\cdots\!20\)\( T^{7} + \)\(10\!\cdots\!81\)\( T^{8} \)
$83$ \( 1 + \)\(19\!\cdots\!00\)\( T + \)\(16\!\cdots\!20\)\( T^{2} + \)\(86\!\cdots\!00\)\( T^{3} + \)\(18\!\cdots\!78\)\( T^{4} + \)\(10\!\cdots\!00\)\( T^{5} + \)\(22\!\cdots\!80\)\( T^{6} + \)\(29\!\cdots\!00\)\( T^{7} + \)\(17\!\cdots\!21\)\( T^{8} \)
$89$ \( 1 + \)\(60\!\cdots\!40\)\( T + \)\(42\!\cdots\!56\)\( T^{2} + \)\(15\!\cdots\!80\)\( T^{3} + \)\(56\!\cdots\!26\)\( T^{4} + \)\(12\!\cdots\!20\)\( T^{5} + \)\(28\!\cdots\!76\)\( T^{6} + \)\(33\!\cdots\!60\)\( T^{7} + \)\(44\!\cdots\!41\)\( T^{8} \)
$97$ \( 1 + \)\(80\!\cdots\!00\)\( T + \)\(80\!\cdots\!80\)\( T^{2} + \)\(38\!\cdots\!00\)\( T^{3} + \)\(20\!\cdots\!18\)\( T^{4} + \)\(59\!\cdots\!00\)\( T^{5} + \)\(19\!\cdots\!20\)\( T^{6} + \)\(30\!\cdots\!00\)\( T^{7} + \)\(59\!\cdots\!81\)\( T^{8} \)
show more
show less