[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8023.1");
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 dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion .
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.
Refresh table
\( p \)
Sign
\(71\)
\(1\)
\(113\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{172} - 24 T_{2}^{171} + 26 T_{2}^{170} + 3928 T_{2}^{169} - 26629 T_{2}^{168} + \cdots + 45656199476103 \)
T2^172 - 24*T2^171 + 26*T2^170 + 3928*T2^169 - 26629*T2^168 - 272224*T2^167 + 3295322*T2^166 + 8278112*T2^165 - 226770243*T2^164 + 138511518*T2^163 + 10608368140*T2^162 - 28269524665*T2^161 - 363232288638*T2^160 + 1655857222183*T2^159 + 9300221128301*T2^158 - 64588199034303*T2^157 - 171875822092679*T2^156 + 1929382723239450*T2^155 + 1828085890368716*T2^154 - 46658799475954991*T2^153 + 12219441254930840*T2^152 + 939904663508029269*T2^151 - 1176709272173417035*T2^150 - 16016304035904681922*T2^149 + 34901481507789720898*T2^148 + 232337476870428593008*T2^147 - 737448257967426449947*T2^146 - 2860102848820122647495*T2^145 + 12621334783561386140803*T2^144 + 29327198898474767930765*T2^143 - 183529220509298202415097*T2^142 - 236630354208665244070122*T2^141 + 2322217642504985647461848*T2^140 + 1204247421370123896248046*T2^139 - 25923273066207971879430384*T2^138 + 2809683862779015844009057*T2^137 + 257469791148723000595999558*T2^136 - 169678169021540238927288506*T2^135 - 2286409775037254631793959390*T2^134 + 2697301917491289058261642252*T2^133 + 18192152940923843039410513452*T2^132 - 31128451604771248446253153557*T2^131 - 129583308117778751519294348494*T2^130 + 298058086036623993911324371442*T2^129 + 822378254297891278535125418395*T2^128 - 2481352495831836861897799415903*T2^127 - 4597136498408132767597156033851*T2^126 + 18365988908990307524450552838255*T2^125 + 22066730740421133620766070336245*T2^124 - 122378323697082187705666714698651*T2^123 - 85280863054764059162861619634261*T2^122 + 739739607078110279931488669990739*T2^121 + 208342203722969639278501050659573*T2^120 - 4076115383699325821543054648000515*T2^119 + 318590127607352690490728435342496*T2^118 + 20536124847184430090299679065284826*T2^117 - 8325179276215253591956730387729094*T2^116 - 94754542716429921001451290964830808*T2^115 + 68003561200965918562996198060627733*T2^114 + 400549394953287444516598066576762685*T2^113 - 413007302501887129563681479379879422*T2^112 - 1549813552467395009136479338329465835*T2^111 + 2112901027797132290155977133874022219*T2^110 + 5474497709428760589816653251057853127*T2^109 - 9512958747109321387944511906845882926*T2^108 - 17565882133963429541078287547232365246*T2^107 + 38476966815805539933585194179148965464*T2^106 + 50732901827493917061264943182244705733*T2^105 - 141391163616560863897914513864269270646*T2^104 - 129635536776593449693822715787772929515*T2^103 + 475221008165175627758046079055011776590*T2^102 + 282584583603242934828605013369922691759*T2^101 - 1467015963435888271535222514125920988472*T2^100 - 476376058507434916016119657942584327675*T2^99 + 4170281559303282644491831974260445126694*T2^98 + 374995236489785074910424250133302589806*T2^97 - 10932893621348435270910282251891372920267*T2^96 + 1329947167016909533285142194241058332360*T2^95 + 26449800973641792873469601029119301470170*T2^94 - 8437244906577319782766938506312760612523*T2^93 - 59045026112965855400777268414774579031455*T2^92 + 30099526678460903201088783828561842938018*T2^91 + 121521844327774862616533303841596785160889*T2^90 - 85238897259067634427039668275591104449744*T2^89 - 230203108193977212787294824121327554754561*T2^88 + 207713757045332231707255100315294231662742*T2^87 + 400284927160467974068574030768158576786887*T2^86 - 449597743775578807729787031264314887281099*T2^85 - 636191163437846484594707024872348669736088*T2^84 + 877906538552502820888481399340285121718731*T2^83 + 918089995105946657719741002181859257311942*T2^82 - 1559617092978649412321446797949107139188129*T2^81 - 1189977661009017465744325151154986421321438*T2^80 + 2533091227957349829450982588359583264342245*T2^79 + 1358617800331362246003107512354859973222328*T2^78 - 3771907472481960882699971627986299858331186*T2^77 - 1312269974370506955172236609195421430772088*T2^76 + 5156852880815164572780984065414060933829009*T2^75 + 960419922795294619943750666588531581510017*T2^74 - 6476668153922076171604900501594388664124742*T2^73 - 282085342554824812918169739641100073263579*T2^72 + 7470971484384377460266428905504912580791856*T2^71 - 641493422866839930212778417997502638636524*T2^70 - 7908749247856582063348062404261133185471956*T2^69 + 1633473047532996532848921722985265955028098*T2^68 + 7672485076870300570913857911576114913646444*T2^67 - 2473765133393824591496691130113585765474069*T2^66 - 6807479285832303255793161595010947601862910*T2^65 + 2977393968373499218573870621273076751314290*T2^64 + 5508988796006912127413907647757184960133412*T2^63 - 3061279243565352765636649840554090502323510*T2^62 - 4051429743524942360822994258629186457755406*T2^61 + 2766299771018520834873112571734254716950504*T2^60 + 2694358098190421910059702418685767386831410*T2^59 - 2226645389565313009743677377309194520127011*T2^58 - 1609245897387450827572566027749197811273555*T2^57 + 1607308907332898188972705600685842738049143*T2^56 + 854446501074665274209016865961723348192764*T2^55 - 1043946419711129289678240258854042399936572*T2^54 - 396731765452769088980438798202165154046076*T2^53 + 610843344182999806188891008712617450375002*T2^52 + 156267695805382478304869551092852022371598*T2^51 - 321965287908160064866911975518750300429265*T2^50 - 48693723598712108354536696055861404781235*T2^49 + 152701418546951900128477484526029903337229*T2^48 + 9323997015703528596567443618297945660873*T2^47 - 65045302352709452300753655633052948018299*T2^46 + 1199706530508232514561215274414933118451*T2^45 + 24820358002375283873502196878961885183211*T2^44 - 2236669865322077397046052898866769505201*T2^43 - 8456767890545259145365951346056368996422*T2^42 + 1321628281949311329059413024321123794538*T2^41 + 2562568515959350859471550040956525477947*T2^40 - 561315528344909982099676913912987998021*T2^39 - 687269061659540756357230202491380433965*T2^38 + 192801111456290995875470726851850056419*T2^37 + 162182824852902648749835438418616638545*T2^36 - 55661281123490847791169462733405169973*T2^35 - 33429597604284751882614260604365377464*T2^34 + 13716072021436666143796379156680253337*T2^33 + 5962146573105900901430530984078293420*T2^32 - 2901879413844339820002459842133432750*T2^31 - 908272138970920087924133131290879260*T2^30 + 527577876843936854720866109457960018*T2^29 + 115941333199757280648482823167259737*T2^28 - 82238376609238249214453923299962131*T2^27 - 12004356995060484882441272980735553*T2^26 + 10940176535175839915088480638936534*T2^25 + 941378354748440736635534002192241*T2^24 - 1233554079292464511451945596790412*T2^23 - 44794148825210112040750802124458*T2^22 + 116805927802382658797136008583193*T2^21 - 680762589729277756291244303970*T2^20 - 9176429748911650117515237500128*T2^19 + 388617269833840135597792412977*T2^18 + 588607317447632966794510605533*T2^17 - 44102727307807014254685711755*T2^16 - 30164687739939308207467037069*T2^15 + 3175003783833024303748417435*T2^14 + 1197661907861898804720050330*T2^13 - 162345692078562152396048174*T2^12 - 35144419386318262299348195*T2^11 + 5968719984503841615630442*T2^10 + 701404849832698171239197*T2^9 - 153378179944088109732974*T2^8 - 7812629655717488526676*T2^7 + 2576307463133975190106*T2^6 + 9977310976299006972*T2^5 - 24680940018278929392*T2^4 + 747088931661016527*T2^3 + 94799924947325292*T2^2 - 5374813517379433*T2 + 45656199476103
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\).