[N,k,chi] = [3467,2,Mod(1,3467)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3467, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3467.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
The algebraic q q q -expansion of this newform has not been computed, but we have computed the trace expansion .
For each embedding ι m \iota_m ι m of the coefficient field, the values ι m ( a n ) \iota_m(a_n) ι m ( a n ) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
p p p
Sign
3467 3467 3 4 6 7
− 1 -1 − 1
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
T 2 162 − 9 T 2 161 − 216 T 2 160 + 2166 T 2 159 + 22307 T 2 158 + ⋯ + 88 ⋯ 56 T_{2}^{162} - 9 T_{2}^{161} - 216 T_{2}^{160} + 2166 T_{2}^{159} + 22307 T_{2}^{158} + \cdots + 88\!\cdots\!56 T 2 1 6 2 − 9 T 2 1 6 1 − 2 1 6 T 2 1 6 0 + 2 1 6 6 T 2 1 5 9 + 2 2 3 0 7 T 2 1 5 8 + ⋯ + 8 8 ⋯ 5 6
T2^162 - 9*T2^161 - 216*T2^160 + 2166*T2^159 + 22307*T2^158 - 254974*T2^157 - 1454004*T2^156 + 19566982*T2^155 + 66135242*T2^154 - 1100821508*T2^153 - 2162210903*T2^152 + 48407962983*T2^151 + 48376883234*T2^150 - 1732427895106*T2^149 - 501906498654*T2^148 + 51874969857018*T2^147 - 13645000875733*T2^146 - 1326044642104577*T2^145 + 946698755132954*T2^144 + 29380487719929051*T2^143 - 32214880325443425*T2^142 - 570954869010080519*T2^141 + 817927572039531502*T2^140 + 9823753797513790836*T2^139 - 17068209192145962382*T2^138 - 150796936914420076687*T2^137 + 304980258603636155329*T2^136 + 2078007459672093415269*T2^135 - 4772458122305720824835*T2^134 - 25837918522497058915510*T2^133 + 66347592451229906333904*T2^132 + 291099217075749693301912*T2^131 - 827701595368252025472947*T2^130 - 2981766580298998058272607*T2^129 + 9335266276511215704968372*T2^128 + 27843692886500539867340332*T2^127 - 95741338290520446491473393*T2^126 - 237512175593856622992404418*T2^125 + 897029037559507404128328674*T2^124 + 1853314952603868002749900538*T2^123 - 7707198141625838270198553473*T2^122 - 13237473778216496432920598828*T2^121 + 60917309458943210645388976589*T2^120 + 86531766135944211821244932961*T2^119 - 444111834320509043546632183959*T2^118 - 517020402686068637287315117797*T2^117 + 2993153835388904600726614419601*T2^116 + 2815587263440679240330215282199*T2^115 - 18684588127661141356580132663303*T2^114 - 13901127540812389541831037651020*T2^113 + 108209831018419504755923257348477*T2^112 + 61621320042335210548570075641326*T2^111 - 582217553681861823359401875546826*T2^110 - 240716451111586421122586008688471*T2^109 + 2913771273596672149244969253765720*T2^108 + 795592524854315953709535045154621*T2^107 - 13577311049147178629882941276723286*T2^106 - 1981138519125853273577712324555197*T2^105 + 58955704515118993710284075481954943*T2^104 + 1777385384488386719751118919305469*T2^103 - 238722484876963986774375492407803258*T2^102 + 18102552306328540033697842859362969*T2^101 + 901902725402291853979994599580526389*T2^100 - 156327654948284524592771358653298898*T2^99 - 3180642632290787918396691361108711817*T2^98 + 837947369740191763208565044389779637*T2^97 + 10473675505610179672784994688941934596*T2^96 - 3635682728893112184129160022255557115*T2^95 - 32211148277035037260280875523341173115*T2^94 + 13694412912292217479269820259726501346*T2^93 + 92530761113220147280872930777472247983*T2^92 - 46097970705979225409891410204420559284*T2^91 - 248283171377201305862838079008543005642*T2^90 + 140739082244167708271271905149614111932*T2^89 + 622240550222394650600919934910141553867*T2^88 - 393023945715526858622629047067019386964*T2^87 - 1456296180630378695329590541057121430898*T2^86 + 1009160177521916598612053653454615740995*T2^85 + 3182110017090244304398673810970398259964*T2^84 - 2390521612301112878236549740170962519816*T2^83 - 6489524351087283885814741198642492722229*T2^82 + 5235589717718125612194752278986291079833*T2^81 + 12347140092576330522096479552607725769793*T2^80 - 10616715850178593417059857386373821350844*T2^79 - 21906144940864592376249173908511911743371*T2^78 + 19949820690078086957238422997009310004168*T2^77 + 36221760734180848206398696487324785022551*T2^76 - 34754164892216517527742882316777759531865*T2^75 - 55783279955315479487697967898295209320915*T2^74 + 56137105925980963607830442703682056658190*T2^73 + 79958861166994661570952662259504138390140*T2^72 - 84064359822789083511289197436459138641472*T2^71 - 106592424832664344658237377587513610533239*T2^70 + 116664961966704000837074469061144273629957*T2^69 + 132046323409726505215250007097753002874297*T2^68 - 149968382907478034378085175167015677805858*T2^67 - 151874842779820431602333348308867937028933*T2^66 + 178434068357503254222639242618824487741541*T2^65 + 162032952997185461684037724957376147018852*T2^64 - 196332291566523749164207960321779954094104*T2^63 - 160198923860523555488367523462148695445559*T2^62 + 199567860142670528624751484283525566091686*T2^61 + 146629476380166201103951217731227528686060*T2^60 - 187178760863589532792004448702504891001854*T2^59 - 124120854887258195719918341000309699465889*T2^58 + 161772546650992768919732551471130747056679*T2^57 + 97068736652755146419509885406308517062421*T2^56 - 128641779903949390364397719107039718164176*T2^55 - 70059947057067833208167276821496837022166*T2^54 + 93964455478445035276752188403645677801185*T2^53 + 46618260653032313216563352036472199190163*T2^52 - 62928798351811262380510850224027546900376*T2^51 - 28567338517120501604180192154881288759463*T2^50 + 38561896255767199652611949421564252180863*T2^49 + 16103659005695915930354664252865977514761*T2^48 - 21573506819490760396474330063122331968935*T2^47 - 8340620512036086525742810250534179607758*T2^46 + 10991800475705248193941371605986317292100*T2^45 + 3963744882954694024693538311258269419641*T2^44 - 5086568532693306570969248066684605732683*T2^43 - 1725673988505128296090400427168415217608*T2^42 + 2131502899513471693876345248500295306217*T2^41 + 686938598980534987407090140301081019179*T2^40 - 806128878037904326344064268195801812192*T2^39 - 249421969651864856453234232275320321676*T2^38 + 274134974058563596297734160875553151189*T2^37 + 82355440223858059563896589365757550940*T2^36 - 83473809518139761042171391216812613048*T2^35 - 24634858842873856504937795307861283185*T2^34 + 22652034867637172519088689640905649455*T2^33 + 6645039612382972586348348642381465499*T2^32 - 5448668249484962152257610751614435477*T2^31 - 1607384639251320260008044641831117860*T2^30 + 1154506017712666129532273676992756916*T2^29 + 346394798612572825111170030316015117*T2^28 - 213929531834565534213411841660683997*T2^27 - 66001067478965555884266677986639439*T2^26 + 34370114263366263826168094761366706*T2^25 + 11022111650463576181036282950765439*T2^24 - 4738366215012256783556025906358646*T2^23 - 1597217252566276441052378193939995*T2^22 + 553435204164804515567435145098836*T2^21 + 198536188525461318483934023019032*T2^20 - 53881649746167968879057114663443*T2^19 - 20886053977932308974819581938087*T2^18 + 4279368387153740823163381887564*T2^17 + 1830191958543511914621848254308*T2^16 - 268900840948137704531514392344*T2^15 - 131031237981038422151300212288*T2^14 + 12737848517740775260429379264*T2^13 + 7482522657823034872800089408*T2^12 - 414518530117440343150190336*T2^11 - 330435767806058253332496896*T2^10 + 7004886351529682186165248*T2^9 + 10827461096408083312863232*T2^8 + 58885501084968521283584*T2^7 - 248330281684969738424320*T2^6 - 5985578380093676601344*T2^5 + 3646393434162337710080*T2^4 + 121964451648670629888*T2^3 - 29282021403863547904*T2^2 - 872000088462983168*T2 + 88061951593414656
acting on S 2 n e w ( Γ 0 ( 3467 ) ) S_{2}^{\mathrm{new}}(\Gamma_0(3467)) S 2 n e w ( Γ 0 ( 3 4 6 7 ) ) .