LMFDB - Newform orbit 444.2.bh.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(19,444)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("444.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([18, 0, 35])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [228,0,0,6,6,0,0,6,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) = $ $ 228 q + 6 q^{4} + 6 q^{5} + 6 q^{8} + 12 q^{12} + 30 q^{14} - 6 q^{16} + 6 q^{18} + 30 q^{20} - 72 q^{22} - 30 q^{25} - 114 q^{27} + 60 q^{32} + 12 q^{37} - 84 q^{38} + 12 q^{39} - 36 q^{40} + 48 q^{43}+ \cdots + 6 q^{98}+O(q^{100}) $

228 * q + 6 * q^4 + 6 * q^5 + 6 * q^8 + 12 * q^12 + 30 * q^14 - 6 * q^16 + 6 * q^18 + 30 * q^20 - 72 * q^22 - 30 * q^25 - 114 * q^27 + 60 * q^32 + 12 * q^37 - 84 * q^38 + 12 * q^39 - 36 * q^40 + 48 * q^43 - 30 * q^44 + 30 * q^46 + 36 * q^49 + 48 * q^56 - 12 * q^58 - 36 * q^60 - 12 * q^62 - 162 * q^64 + 54 * q^65 + 6 * q^66 + 24 * q^67 - 72 * q^68 - 132 * q^70 + 72 * q^74 - 78 * q^76 - 48 * q^77 - 30 * q^78 - 132 * q^80 - 102 * q^82 + 24 * q^84 - 240 * q^86 - 36 * q^87 - 108 * q^88 - 36 * q^91 + 54 * q^92 + 24 * q^93 - 48 * q^94 + 66 * q^96 + 6 * q^98

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment:embeddings in the coefficient field

gp:mfembed(f)

Label	$ a_{2} $			$ a_{3} $			$ a_{4} $			$ a_{5} $			$ a_{6} $			$ a_{7} $			$ a_{8} $			$ a_{9} $			$ a_{10} $
19.1	−1.41336	+	0.0492507i	0.766044	−	0.642788i	1.99515	−	0.139217i	0.872865	+	1.87186i	−1.05104	+	0.946216i	0.881134	−	2.42090i	−2.81300	+	0.295026i	0.173648	−	0.984808i	−1.32586	−	2.60262i
19.2	−1.33196	+	0.475271i	0.766044	−	0.642788i	1.54823	−	1.26608i	−0.494638	−	1.06075i	−0.714842	+	1.22025i	−1.62491	+	4.46441i	−1.46045	+	2.42220i	0.173648	−	0.984808i	1.16298	+	1.17780i
19.3	−1.19786	−	0.751754i	0.766044	−	0.642788i	0.869731	+	1.80099i	0.992176	+	2.12773i	−1.40083	+	0.194092i	−0.718808	+	1.97491i	0.312087	−	2.81116i	0.173648	−	0.984808i	0.411042	−	3.29459i
19.4	−1.15570	−	0.815087i	0.766044	−	0.642788i	0.671267	+	1.88399i	−1.57207	−	3.37132i	−1.40924	+	0.118475i	−0.308040	+	0.846332i	0.759830	−	2.72446i	0.173648	−	0.984808i	−0.931080	+	5.17760i
19.5	−1.12501	+	0.856939i	0.766044	−	0.642788i	0.531310	−	1.92814i	−0.500408	−	1.07313i	−0.310980	+	1.37960i	0.492962	−	1.35440i	1.05456	+	2.62448i	0.173648	−	0.984808i	1.48257	+	0.778465i
19.6	−0.696269	+	1.23094i	0.766044	−	0.642788i	−1.03042	−	1.71413i	1.72680	+	3.70313i	0.257859	+	1.39051i	−0.516823	+	1.41996i	2.82744	−	0.0748897i	0.173648	−	0.984808i	−5.76064	−	0.452791i
19.7	−0.551076	−	1.30243i	0.766044	−	0.642788i	−1.39263	+	1.43547i	0.121266	+	0.260055i	−1.25933	−	0.643492i	−1.13724	+	3.12455i	2.63704	+	1.02275i	0.173648	−	0.984808i	0.271877	−	0.301250i
19.8	−0.271472	+	1.38791i	0.766044	−	0.642788i	−1.85261	−	0.753558i	−0.251570	−	0.539494i	0.684174	+	1.23770i	−0.241047	+	0.662271i	1.54880	−	2.36669i	0.173648	−	0.984808i	0.817065	−	0.202700i
19.9	−0.183987	−	1.40219i	0.766044	−	0.642788i	−1.93230	+	0.515972i	−1.38572	−	2.97168i	−1.04226	−	0.955878i	1.24511	−	3.42090i	1.07901	+	2.61452i	0.173648	−	0.984808i	−3.91192	+	2.48980i
19.10	0.370052	−	1.36494i	0.766044	−	0.642788i	−1.72612	−	1.01020i	1.79643	+	3.85246i	−0.593891	−	1.28347i	1.26029	−	3.46263i	−2.01761	+	1.98223i	0.173648	−	0.984808i	5.92315	−	1.02641i
19.11	0.474108	+	1.33237i	0.766044	−	0.642788i	−1.55044	+	1.26338i	0.516721	+	1.10811i	1.21962	+	0.715907i	−0.551476	+	1.51517i	−2.41837	−	1.46679i	0.173648	−	0.984808i	−1.23144	+	1.21383i
19.12	0.554281	+	1.30107i	0.766044	−	0.642788i	−1.38555	+	1.44231i	−1.12466	−	2.41185i	1.26091	+	0.640389i	1.25426	−	3.44605i	−2.64452	−	1.00324i	0.173648	−	0.984808i	2.51459	−	2.80010i
19.13	0.695075	−	1.23161i	0.766044	−	0.642788i	−1.03374	−	1.71213i	−0.333767	−	0.715766i	−0.259207	−	1.39026i	0.214477	−	0.589271i	−2.82721	+	0.0831102i	0.173648	−	0.984808i	−1.11354	−	0.0864394i
19.14	1.08730	+	0.904316i	0.766044	−	0.642788i	0.364424	+	1.96652i	1.25263	+	2.68628i	1.41420	−	0.00615390i	1.15471	−	3.17253i	−1.38212	+	2.46774i	0.173648	−	0.984808i	−1.06726	+	4.05355i
19.15	1.24254	−	0.675354i	0.766044	−	0.642788i	1.08779	−	1.67830i	−1.74811	−	3.74884i	0.517729	−	1.31604i	−0.960308	+	2.63843i	0.218173	−	2.82000i	0.173648	−	0.984808i	−4.70389	−	3.47747i
19.16	1.27151	−	0.619084i	0.766044	−	0.642788i	1.23347	−	1.57434i	1.30887	+	2.80688i	0.576093	−	1.29156i	−1.17979	+	3.24145i	0.593721	−	2.76541i	0.173648	−	0.984808i	3.40193	+	2.75867i
19.17	1.33172	+	0.475940i	0.766044	−	0.642788i	1.54696	+	1.26764i	−0.999025	−	2.14242i	1.32609	−	0.491423i	0.604828	−	1.66175i	1.45680	+	2.42440i	0.173648	−	0.984808i	−0.310762	−	3.32858i
19.18	1.35146	−	0.416594i	0.766044	−	0.642788i	1.65290	−	1.12602i	0.333042	+	0.714211i	0.767498	−	1.18783i	1.24222	−	3.41298i	1.76474	−	2.21036i	0.173648	−	0.984808i	0.747630	+	0.826485i
19.19	1.35436	+	0.407058i	0.766044	−	0.642788i	1.66861	+	1.10261i	0.331199	+	0.710258i	1.29916	−	0.558745i	−0.873976	+	2.40123i	1.81108	+	2.17256i	0.173648	−	0.984808i	0.159448	+	1.09677i
55.1	−1.38205	−	0.299903i	0.766044	−	0.642788i	1.82012	+	0.828962i	−0.984369	+	0.459019i	−1.25148	+	0.658624i	−0.462373	+	1.27036i	−2.26688	−	1.69153i	0.173648	−	0.984808i	1.49811	−	0.339171i

See next 80 embeddings (of 228 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
148.q	even	36	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	444.2.bh.b	yes	228
4.b	odd	2	1		444.2.bh.a	✓	228
37.i	odd	36	1		444.2.bh.a	✓	228
148.q	even	36	1	inner	444.2.bh.b	yes	228

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
444.2.bh.a	✓	228	4.b	odd	2	1
444.2.bh.a	✓	228	37.i	odd	36	1
444.2.bh.b	yes	228	1.a	even	1	1	trivial
444.2.bh.b	yes	228	148.q	even	36	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{7}^{228} - 18 T_{7}^{226} + 255 T_{7}^{224} - 1368 T_{7}^{223} - 42620 T_{7}^{222} + \cdots + 21\!\cdots\!36 $ T7^228 - 18*T7^226 + 255*T7^224 - 1368*T7^223 - 42620*T7^222 - 24840*T7^221 + 650865*T7^220 + 541512*T7^219 - 6170838*T7^218 + 63486360*T7^217 + 1095930077*T7^216 + 1283206848*T7^215 - 13083371958*T7^214 - 18565086312*T7^213 + 78714275877*T7^212 - 1517323875624*T7^211 - 19073952076122*T7^210 - 35539126780224*T7^209 + 143250133766241*T7^208 + 364672556780184*T7^207 + 98132520452130*T7^206 + 25401994007229384*T7^205 + 250756280970364372*T7^204 + 634863750717725136*T7^203 - 564029112480790146*T7^202 - 3055054678421174136*T7^201 - 10904447350591619841*T7^200 - 307000085544546989544*T7^199 - 2569133216226511694302*T7^198 - 8023341901627940618808*T7^197 - 7382312630873499966072*T7^196 + 3042087094418437076400*T7^195 + 133073616833861875796334*T7^194 + 2755416257086200855446352*T7^193 + 20994273457936487736756583*T7^192 + 76855775311014625477069368*T7^191 + 164061725384692678555517238*T7^190 + 305754030384727547026254360*T7^189 - 438008037348758253278059560*T7^188 - 17131158132847659614266091424*T7^187 - 131016477464906026665492543338*T7^186 - 540646521804767462117593537944*T7^185 - 1560793294345539348012897788031*T7^184 - 3902720487501158513925863400312*T7^183 - 2973179359074120077820297181626*T7^182 + 74081577695663013898011700130448*T7^181 + 628152382908384405890617376476351*T7^180 + 2895668438595797684560309038500904*T7^179 + 9937472689457169336520903371737424*T7^178 + 29043931047605404650856909371576120*T7^177 + 51299808736111449186118409575465212*T7^176 - 176351103858934761757415694560718456*T7^175 - 2151785696618201292051795049078721630*T7^174 - 11226758040509083409836301363947875168*T7^173 - 43087685972918169990044896135597447566*T7^172 - 137634387113553834510840078885139977672*T7^171 - 310515935721907467002564849843924407518*T7^170 + 83356078646704059394357836925845500232*T7^169 + 5358072707209597812641039889698596903193*T7^168 + 32724178107523759708436721797238462517344*T7^167 + 137648679065385937140091637340273264614256*T7^166 + 469875524288779107493758240733865232764976*T7^165 + 1215324851243969867524336116166602181991310*T7^164 + 1272952904522442224930790987057030357333552*T7^163 - 8548867410578883206118137874631352846974726*T7^162 - 68392449396354652851853596449955124783657440*T7^161 - 314563989843316039985603162640595524627259959*T7^160 - 1124913030598400225089413634183438874658244224*T7^159 - 3106975652660451451994066226901125876128604738*T7^158 - 4930126896426107854028250925767570170444402520*T7^157 + 8700823976989529403640244125253518675520812234*T7^156 + 109578143549866227884302675482307559044246609344*T7^155 + 548008603492503439650251796311517494399665819368*T7^154 + 2021065670383567567475772167389687041458376280776*T7^153 + 5770135363926354637894801015722773145934477472556*T7^152 + 10761694188066325606071800750213705283006612835632*T7^151 - 2856634567433812626696447370414149613389169780918*T7^150 - 133446728636053967480439114309307177119961265930976*T7^149 - 726223465868339744768304146801344626715320750580257*T7^148 - 2730600781336700954267302635188407875604179806108352*T7^147 - 7894490129817252195312791607043694536703938514573172*T7^146 - 15816084481811262632464679334436309537021248088614840*T7^145 - 6115116954792178881883009675390154622073723139949736*T7^144 + 126123391066025019420604460485882428406239450389497344*T7^143 + 748185370793187011658758264251035993248010903402817728*T7^142 + 2852288073660452419647741545540203263048645811596541824*T7^141 + 8283745708144366130531517675667827589069661371860087399*T7^140 + 17296424341497783956211676863173119850306316905211374880*T7^139 + 13609852724946677925559514808301720425737115615414734724*T7^138 - 89198657101557221194340805042754322892999261446747153064*T7^137 - 591067065855789168469232072993005672342478233509771380784*T7^136 - 2284471647979388107643768129403932520780414523377562556496*T7^135 - 6636066192461577717046786575529217333608523030580517053060*T7^134 - 14191305240432334344627663167450117251575256741983886811424*T7^133 - 14895696204003721889266019434556952098882404938354741063767*T7^132 + 46164820644867704977505173957974127415223043018539024085440*T7^131 + 358385960420521338389464881910248456953735473103733818078790*T7^130 + 1414693237466734743601858056965874540908933179366241313364320*T7^129 + 4128558837109309605906658991848481465998970782872623561508567*T7^128 + 9035140537551012961697068592199827321605822080980451436428504*T7^127 + 11476785052640168910725674009514255154870950226068121232062732*T7^126 - 15085768707624461754842362933641120051833298228711186206240424*T7^125 - 161657014336886178809334206134067663827614981551437559961747045*T7^124 - 661971731826681635192596323785408692072959615072722217128413224*T7^123 - 1950512105030620598466279713331297700959338585648216143649850294*T7^122 - 4360990319236645174435072864014358310407263676362717203890532616*T7^121 - 6302318385121718855778090373835200706929516940222499677904838531*T7^120 + 1949401961575208546878833308263891635353105632177731021170677392*T7^119 + 53806608975340269917946879354389733148127251491330948711887866218*T7^118 + 234716535608328062230736756524164852158750243897750516870690616264*T7^117 + 706146803495106725755475932075848878800223386191143661950932108398*T7^116 + 1625354917466672038569471367890492794734645406644913993369474839224*T7^115 + 2633076963190279651894658087637184555713366338192264824433201702980*T7^114 + 1129705824641095639273213259395796704557804152285297877631362460752*T7^113 - 11975782784218966364360788699807713165845627226418046151916710870900*T7^112 - 59991220502832317888346113008911146374703815445836883891075952248688*T7^111 - 187898012295611042935360499349904986699618686924269138519670887443522*T7^110 - 448042761628285186636031304032474287512784272421160746294127466896880*T7^109 - 795819572765187419406644271460043395794892438909022898873489461138883*T7^108 - 737004445605054463902129539542921276069909356464845549561295045353080*T7^107 + 1540125591318106543643370759278292198452931729179762352311027532571008*T7^106 + 10774570126209215633028863957909581263081597372167245574165671793912256*T7^105 + 36486379871126628262457740172054797304817671729930592233920356009753240*T7^104 + 91895108595317293322069142119764257933627126664315653118845869272026984*T7^103 + 179911789527570193588262778287940063296460975743535405420595601937211012*T7^102 + 243438585884041867625118088221537279873154551714015438325573068899098752*T7^101 + 41648535890134151355909012336525368086036951122550990010916477871071198*T7^100 - 1084883945000082104099943122563754810753151080384999590159884978409061112*T7^99 - 4521881795530433785337275163720096193846405273776506307901391902950873526*T7^98 - 12448046511337063755749403323886009042268499525037953367609277030498676160*T7^97 - 26669972742552538078277601186504967861826059553189728393655566672422445389*T7^96 - 43988751723494166089188648958210904384789989032763370122622657011414561208*T7^95 - 44263900462310756883692689786663896805337196224252035658261977160530145244*T7^94 + 33261855175908842152385731729718504036537532087567534379406972294712496632*T7^93 + 325782757841517588510317568597733628282766981242801927185152854184158759907*T7^92 + 1079501243627289368035655288829647146477524302004070068663183119520819888888*T7^91 + 2626248661142108824642868555864601643485359957733675551987762419660544609386*T7^90 + 5188094385320723308196300673235345295200878410821040304382256492874181360776*T7^89 + 8323688422170953879197459808605969376256386666339468496723741798424710448131*T7^88 + 9826269246897596557257978194891300936175376199186756868376145051602958131728*T7^87 + 4099765140286406898670590639645753072125415347886440855405122226712400703826*T7^86 - 19292945306125355421768910698080081625881088325230296242046140562466045064320*T7^85 - 74902524250608747099880842530855891274126959109780419642414103085831428620689*T7^84 - 174681874924554376420139838562271032684159631762008080573902516531018028308112*T7^83 - 310166013323459266246985919860618160687736561417146298215211460411145970468242*T7^82 - 419687004787988587397248342717891847682647113099352450005213539915636518230344*T7^81 - 343408188184210771576875568214665395270209368770673168258110385775860858162047*T7^80 + 216998324894739123434108595597886577049247870563807317648457593139185880750480*T7^79 + 1697568466205696731444443007576978666384101673225162498659895009466307642513274*T7^78 + 4578093362951441182386187136488858766619269580364246606958514013756078204713768*T7^77 + 9149241210889330181232124291937295243491704966739209641541836729746571558067845*T7^76 + 15144300424644029609942979723291516298706464155297489540505769648527684657146864*T7^75 + 21335526781523095139971096217049608582915728542008069740958238708707711797249164*T7^74 + 25313278374865086970359681530138987350008679174233245257126095742176987730290288*T7^73 + 23741038605747700698960262590661816219028654371793198568603340591273099806953360*T7^72 + 13316574510325162008612006663775911629970931728835151710592180079241639355512368*T7^71 - 7588821629915133123897947919208235241857752045685376118048006550962162692092970*T7^70 - 37084571760451237067146208530319659917481860083056637756039687123938569327184032*T7^69 - 68573695188137881015547994645730296592412343780479584502393712955622341293350121*T7^68 - 91177083562760271260210955669548630902798887729267929614920368766821321903007168*T7^67 - 92300599820054209807145112374552249212698429937565498950833597579510754268713112*T7^66 - 61954528536191634265105857951149508654746505009428000807962208125736970522332328*T7^65 + 2506590098879718062715090947954495061562306020025265359746113582727036769069746*T7^64 + 93321189795433774362733061843749709095285164122066567683100056072034431571230320*T7^63 + 192633460510070467990036195709675676354788837102725578411700124093162432105224536*T7^62 + 276503492543107771170139500523222271103620491504878872807962242225925827079050192*T7^61 + 321492547732522908359879091759315954554863445078905211852015062945574950235572621*T7^60 + 311535994482431504483674218420338357959212200965839087160505044737215083055677968*T7^59 + 243533927642641623726745956374111992823414280096638654520464830497848941135087188*T7^58 + 129668263207319085704010920368016754622063081957328689388300206725057874760062152*T7^57 - 4927726920247340364443662175820069123638503690071387523714551428456362158750360*T7^56 - 128582252790868142298744470059393807045366452736517444224828075064919017110156944*T7^55 - 212105200441129906257217148005390687999721158016430507744809864616592935233650696*T7^54 - 237073657599130576907901528994187620973952528167667234506681407523353640223317616*T7^53 - 202269070091614831342847032049645426851254795128519344723462055636326410946901580*T7^52 - 124851500004443876178176407474814938333078356021570633421030131709087056052660032*T7^51 - 32590813224153075135833077465755827762645214849596392215953349870271010166968928*T7^50 + 48974842614844269810775869013784358472564480805750208257726177090117966810455392*T7^49 + 105791981812476868794112412011593683038571735498545733572481811754518352435419808*T7^48 + 132952207482218983894275768902369257511349887205024667123398757453351173330049536*T7^47 + 129108544334598616140487284032468677527807806877847853831074428490978378095697632*T7^46 + 97780077035265596237814255637901966330307421266588358694154936116546522897722944*T7^45 + 51457036647940484708982571041561327877345775373304358674739624324964327330909312*T7^44 + 8618285198395878120617796601715200296975329025722951064520647473207975852698368*T7^43 - 18350727764077212834012070010443017443059006305882885640104205717661177791240896*T7^42 - 29282015890048101052093176552943423947412710471456426579164252291568596535978624*T7^41 - 30165920906794722916988602377322577425098542875477514237472404587728368588385408*T7^40 - 25383661331436634028182234281067293631943020697941424747938312057483665085797888*T7^39 - 16531401935568141596583203611875268251007366288081599741260643882527792108344704*T7^38 - 6114311719363808544574677032340628236890317520111872993971074215247924939820288*T7^37 + 2070293202429711422553677249181103833766316184829077356509541217877254855131776*T7^36 + 5960770107036567949594773101935212981097107326034851718561408741055731309530112*T7^35 + 6317647855178848307947105111812057322999363640780354819479013150880119373719808*T7^34 + 5075135968757893946302272533245686147789665903805173194697195257464874499489280*T7^33 + 3521355402680254468019223972587829304595483018660695389470133380741815237933056*T7^32 + 2109863382554644333689259278570585162441801796116749693075171574070303640054784*T7^31 + 1015096958561721589504803735421327121887212374458557924603759499283968480477184*T7^30 + 328298444374466382646777552746979100395579573855115826423963145295911047542784*T7^29 + 8924917255844279129709836222902102033605053308084466907864831312826208517120*T7^28 - 85024885366746502044769147943874523575546688812534418772733734935576089305088*T7^27 - 81211053974547384188530841964428997670784790427714095170531516787228228808704*T7^26 - 48314760939303399231537284709191289153672524457383790924487842200114821232640*T7^25 - 17178077800782020168750575671412279204676878381694942384938332006008545585152*T7^24 + 115432452541181182976920488501183702242899774482311724066270160352400273408*T7^23 + 4293673130364278488965741454859226100246471440594238538961855253557281310720*T7^22 + 2567109696388935483235214203012144809851417311186317258125360127406676484096*T7^21 + 617617874814076113213527480578050733445898000490212169253992295179821760512*T7^20 - 69570199222278495229109945302901284830677537272773296275566017528109244416*T7^19 - 88710041132300428908820153456346443063379447734142497552085428800484450304*T7^18 - 19848041584590022666371518941205811215456386721310597925755635283419750400*T7^17 + 527040808754590772524398765243606303215662743652905638887614190006849536*T7^16 + 213917946061837520330582116200161987663536477848863095179084261684559872*T7^15 - 467853325389991502678233352848916780423992838733324737357366572442591232*T7^14 - 113161141622628086849263010713090039585616082473006636279702722455109632*T7^13 + 44650050399463142778228257790106143220130382222558593388435580525023232*T7^12 + 21368899865744454472286658037355215575869953335563328301011697446518784*T7^11 + 2840797446031566544331770220092341648181727379159181593333720041717760*T7^10 + 577217057357234481939573895068826088598322263990348135168022727884800*T7^9 + 231643202739862941785933918702234752626720404261749454840275245465600*T7^8 + 32891982504670720467211492653630961072854229225038257568184063229952*T7^7 + 2334815284818281961191773128011213172030431532263894942299627454464*T7^6 + 774002916327747858062948043460485118380605045418859795289053593600*T7^5 + 136360865805466032888827037066292534712090860002857064932006952960*T7^4 + 8804681739454149053523586920132378251104820404421062295870767104*T7^3 + 667081300669851492257321225839909539511460421261357477034721280*T7^2 + 135944588977921600182252727113282699509856101708909243579498496*T7 + 21042478233963926394716384960677350279409596541780449229275136 acting on $S_{2}^{\mathrm{new}}(444, [\chi])$.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.bh (of order \(36\), degree \(12\), minimal)

\(n\):		e.g. 2-40 or 80-90
Embeddings:		e.g. 1-3 or 19.19
Significant digits:
Format:

Introduction

L-functions

Modular forms

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