Properties

Label 3.71.b
Level 3
Weight 71
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 22
Newforms 1
Sturm bound 23
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 71 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(23\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{71}(3, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 22 22 0
Eisenstein series 2 2 0

Trace form

\(22q \) \(\mathstrut -\mathstrut 57760946614928610q^{3} \) \(\mathstrut -\mathstrut 12924724784889679105472q^{4} \) \(\mathstrut -\mathstrut 2542746418602623176312578240q^{6} \) \(\mathstrut +\mathstrut 3460300354929279082139211020q^{7} \) \(\mathstrut -\mathstrut 3187627653443587997840864868739482q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut -\mathstrut 57760946614928610q^{3} \) \(\mathstrut -\mathstrut 12924724784889679105472q^{4} \) \(\mathstrut -\mathstrut 2542746418602623176312578240q^{6} \) \(\mathstrut +\mathstrut 3460300354929279082139211020q^{7} \) \(\mathstrut -\mathstrut 3187627653443587997840864868739482q^{9} \) \(\mathstrut -\mathstrut 204904054456738768728763726683461760q^{10} \) \(\mathstrut +\mathstrut 168216518978261501059545818584280696640q^{12} \) \(\mathstrut -\mathstrut 1425273500899614630088058291006011908100q^{13} \) \(\mathstrut -\mathstrut 225789500492205687292660149319768298715840q^{15} \) \(\mathstrut +\mathstrut 7791108876170200924142434286561643963000832q^{16} \) \(\mathstrut -\mathstrut 159240712078782992086911930584730978792685440q^{18} \) \(\mathstrut +\mathstrut 2012529521265601397979311193864856923750823676q^{19} \) \(\mathstrut -\mathstrut 5316334525000974787771605720411010154937122916q^{21} \) \(\mathstrut -\mathstrut 177999664576757911046568099334764110597720653440q^{22} \) \(\mathstrut +\mathstrut 2221044214363105865421794285118261395337437583360q^{24} \) \(\mathstrut -\mathstrut 47913993180689593092577485889381363779493774325690q^{25} \) \(\mathstrut -\mathstrut 327350510975933028532160361074129063579708328041490q^{27} \) \(\mathstrut +\mathstrut 199622305967867855771313967200368144722234985321600q^{28} \) \(\mathstrut +\mathstrut 19529370934845391692884101303550253186745064711003520q^{30} \) \(\mathstrut +\mathstrut 12388430374073163692752061441697409777651574405007404q^{31} \) \(\mathstrut +\mathstrut 91609538538011962010378972773658529100477255901421120q^{33} \) \(\mathstrut +\mathstrut 605761954772905142742127812440233067564260993651653120q^{34} \) \(\mathstrut +\mathstrut 903849673866118209515044215587923561361275075218434112q^{36} \) \(\mathstrut -\mathstrut 2942122339532414491328953596359839081620064777882528420q^{37} \) \(\mathstrut -\mathstrut 83642273913756481299940648535011188445494335818507646004q^{39} \) \(\mathstrut +\mathstrut 272642123044960747425938890972217844718938356564315934720q^{40} \) \(\mathstrut +\mathstrut 1560147154093916143029768098476489647357578674968337342080q^{42} \) \(\mathstrut -\mathstrut 4545359228128189931707988293083620465330530163336481972580q^{43} \) \(\mathstrut -\mathstrut 13684191484560547979485162889557225553655737227535310368640q^{45} \) \(\mathstrut +\mathstrut 34824945738150746982031713560272687284036228683298922087680q^{46} \) \(\mathstrut +\mathstrut 187018310806180504680614747073364302422042767094159794882560q^{48} \) \(\mathstrut +\mathstrut 537429667187009430823177633570141302055322425376808156541794q^{49} \) \(\mathstrut +\mathstrut 93003444735225900297901054333392923286830613776157770499840q^{51} \) \(\mathstrut -\mathstrut 256980181653870794210710907095882776189154704275967737138560q^{52} \) \(\mathstrut +\mathstrut 563860949077651296335542553968680463677661322067851314468800q^{54} \) \(\mathstrut -\mathstrut 3516118540339332578884347645630886351467431915082786354698880q^{55} \) \(\mathstrut +\mathstrut 62619566495727497029128246919971991949893526891401194293093580q^{57} \) \(\mathstrut +\mathstrut 116675137250817318744043251484707490614825810469582794383621760q^{58} \) \(\mathstrut -\mathstrut 289520688194704548710930657842220413516071423272166989563023360q^{60} \) \(\mathstrut -\mathstrut 1004518379975789938184755460502459521248398274882979931600708676q^{61} \) \(\mathstrut +\mathstrut 2259750912371699320668016184778015293200259463243321554460021420q^{63} \) \(\mathstrut -\mathstrut 6990282608978901236062382909358427229318771679854621867713298432q^{64} \) \(\mathstrut +\mathstrut 9802144175872303219237439174047894300074716767326740733265952640q^{66} \) \(\mathstrut -\mathstrut 9530737568144236105810003684427263525901520593033925660073496260q^{67} \) \(\mathstrut +\mathstrut 68660923095126616358914910008665108044130343377859227725343530880q^{69} \) \(\mathstrut -\mathstrut 186825484366209931701114245951001364013348939360625786570907971840q^{70} \) \(\mathstrut +\mathstrut 800859191695150280430684829106757981081528103077118327934086410240q^{72} \) \(\mathstrut -\mathstrut 498564607593670758195755796246723418636521686724391030404386208820q^{73} \) \(\mathstrut +\mathstrut 2109806600351472862056557154002428953234561707550117711339382623630q^{75} \) \(\mathstrut -\mathstrut 5263274864463875706518271175142614969672638525330024503218962553216q^{76} \) \(\mathstrut +\mathstrut 12308167524701892969963937648343555852922730564344320620076689564800q^{78} \) \(\mathstrut -\mathstrut 17307670437682441097149414568687707748355067787533584779481303522964q^{79} \) \(\mathstrut +\mathstrut 13169506853202980530135359556542777642532240836639689883271737852342q^{81} \) \(\mathstrut -\mathstrut 39431820989895068684167150578955043187025954212565254141576902204160q^{82} \) \(\mathstrut +\mathstrut 138763489413867144231869861916118201044140663071190925822310630686336q^{84} \) \(\mathstrut -\mathstrut 61037539079877371876604729964700889725410552523647838067356520814080q^{85} \) \(\mathstrut -\mathstrut 149627312260702067527556548128053547148656320722965526646581032129600q^{87} \) \(\mathstrut +\mathstrut 423107204692289659768926623144292819592688368886126043795359525621760q^{88} \) \(\mathstrut -\mathstrut 954822316211616625813572408526438784570624253142422549351495971955840q^{90} \) \(\mathstrut +\mathstrut 1351237435163715752950727836854267043101210025128484375869461920848568q^{91} \) \(\mathstrut -\mathstrut 1419126662189890378883596636164605113800863195507982624574295260938180q^{93} \) \(\mathstrut +\mathstrut 10138980254856605941232671681032460690110853357766177455228626662453760q^{94} \) \(\mathstrut -\mathstrut 12383253221007478242150050518024370091385337450937902244753056045137920q^{96} \) \(\mathstrut +\mathstrut 5943877415032019678068302054256035030995353737176853716379501144663980q^{97} \) \(\mathstrut -\mathstrut 21983160871333538547745741193506138170867254293489738303957813119108480q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{71}^{\mathrm{new}}(3, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.71.b.a \(22\) \(93.095\) None \(0\) \(-5\!\cdots\!10\) \(0\) \(34\!\cdots\!20\)