Space of modular forms of level 3, weight 71, and Character 3.b

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

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:			\(\Q\)
Newform subspaces:			\( 1 \)
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

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

Decomposition of \(S_{71}^{\mathrm{new}}(3, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.71.b.a	$3$	$71$	3.b	3.b	$2$	$22$	$22$	$93.095$		None		✓	✓	✓	3.71.b.a	$2$	$0$	\(0\)	\(-57\!\cdots\!10\)	\(0\)	\(34\!\cdots\!20\)		$\mathrm{SU}(2)[C_{2}]$