[N,k,chi] = [2,66,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 66, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 66);
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 285120\sqrt{7845027215820649}\).
We also show the integral \(q\)-expansion of the trace form .
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 1149059960205192T_{3} - 7527621327730776295070757798384 \)
T3^2 - 1149059960205192*T3 - 7527621327730776295070757798384
acting on \(S_{66}^{\mathrm{new}}(\Gamma_0(2))\).
$p$
$F_p(T)$
$2$
\( (T + 4294967296)^{2} \)
(T + 4294967296)^2
$3$
\( T^{2} + \cdots - 75\!\cdots\!84 \)
T^2 - 1149059960205192*T - 7527621327730776295070757798384
$5$
\( T^{2} + \cdots - 24\!\cdots\!00 \)
T^2 + 74762585156433859878900*T - 2430418325096812995262050998484955513935937500
$7$
\( T^{2} + \cdots + 16\!\cdots\!44 \)
T^2 - 2708640414989937592480190224*T + 1615553276508109736439343463659980992189123752411822144
$11$
\( T^{2} + \cdots - 19\!\cdots\!16 \)
T^2 - 7814753200781491255136419864110744*T - 19149269991247697257155678576750862774170902602444866548394087068016
$13$
\( T^{2} + \cdots - 21\!\cdots\!04 \)
T^2 - 287941297605631208764186974453740572*T - 211255417488911638345946942549852657919185701628283814525580433528268604
$17$
\( T^{2} + \cdots - 38\!\cdots\!76 \)
T^2 - 3843716467362820505259299926434154902564*T - 3804969037266537495365367207174112930435742037078002803826981399831587899954876
$19$
\( T^{2} + \cdots - 30\!\cdots\!00 \)
T^2 + 139020738020995078570210134727914078802520*T - 309515981638823142970282357635457754414874849031713940727449994535374559185100402800
$23$
\( T^{2} + \cdots + 25\!\cdots\!36 \)
T^2 - 142019031844483932707119538323019471408196912*T + 2589395027981883133458209890122568085244250508744138729133853853685856716755572784118336
$29$
\( T^{2} + \cdots + 75\!\cdots\!00 \)
T^2 - 639934089647120784474016962777338487342778414140*T + 75198065216385015998391624154279534499113903326292107642547214191644644710963175131314672999300
$31$
\( T^{2} + \cdots + 64\!\cdots\!64 \)
T^2 - 300768215796454443684329442990836225518058757184*T + 647593636147042266982519172506596558907670927821634086067950842424943796305835106515525796864
$37$
\( T^{2} + \cdots + 70\!\cdots\!04 \)
T^2 + 2176241718518359453545368103770062923001602562332596*T + 708251510833972943397107137518643121083048072166648927214450802772311152458648811417820332580528682404
$41$
\( T^{2} + \cdots - 58\!\cdots\!56 \)
T^2 + 931180544963876042511133468226601264336111121474476*T - 583293570430454819475100571570610796741658042793522980568486315532805175307752028885179043223143073308956
$43$
\( T^{2} + \cdots + 54\!\cdots\!96 \)
T^2 - 151429462228340538091782829526539465322500240444781272*T + 5439931934769743636558314503999471457771331016322794416445477930994774974427269454904881194990219630622096
$47$
\( T^{2} + \cdots + 22\!\cdots\!04 \)
T^2 + 3096134577792827886363283783109190180392077361634043296*T + 2204852702541563142503645985499452876271289881349067667779960370150069484113279643865823005213174947839797504
$53$
\( T^{2} + \cdots - 61\!\cdots\!64 \)
T^2 + 52517467203838658973387521548817042054580434061656887188*T - 6175180159649814207950032813505800105203032904679240802035209493513411926689131221329586222715751221644560913564
$59$
\( T^{2} + \cdots + 25\!\cdots\!00 \)
T^2 + 6547849095499637425156793635292490662727796465107663699720*T + 2573394858447671561583224580528396077729514701446743734845985063593985008266802094137733850162971558391931512925200
$61$
\( T^{2} + \cdots + 21\!\cdots\!24 \)
T^2 + 29380285502874290381589453783136387793461345099916001346436*T + 215499973362092593761704168992432900748627337976202388184057313305438558338285906226861022211271186937376359534565124
$67$
\( T^{2} + \cdots - 34\!\cdots\!56 \)
T^2 + 164305446435153956172275717805500021581006413404436237174776*T - 3451309245973307624363395047018180773413343331546539241332217228041515504682181172636041745535053723642844883062403056
$71$
\( T^{2} + \cdots - 26\!\cdots\!76 \)
T^2 - 2453534931862245274417979916670078758979367454670633618302864*T - 262151177322248097337296243509961665455813564787313459974684213113752749081420326459927144631027279241394675711725859776
$73$
\( T^{2} + \cdots - 57\!\cdots\!44 \)
T^2 - 2935245778302717865505631748558694768415627550668661201219732*T - 5771677943337944296178295159133319461635312123734667898322068184834328572467637417807985227358917519940344888778959948444
$79$
\( T^{2} + \cdots + 11\!\cdots\!00 \)
T^2 + 72171542937873796885681569856242137791232972883988132641999200*T + 1154500556183261842796627809245807987506251184556304573142896994220205078233970758178232480198438511404031221383471038265600
$83$
\( T^{2} + \cdots + 10\!\cdots\!76 \)
T^2 + 216578296656212841435012106803173057227344789251803461413759448*T + 10187923023870244078188446014013180135804666287188464976655957085699140702493397184482483459738719653863574435431440486476176
$89$
\( T^{2} + \cdots - 23\!\cdots\!00 \)
T^2 + 2678285219425147193448217577130071911144760947065589031199590220*T - 237977493297800085112827113024458660642515330249662586052129732624179240076394510280087317874480186636462703810598507475447900
$97$
\( T^{2} + \cdots - 40\!\cdots\!76 \)
T^2 + 5963019226432002456985859994072397087502966236579822842593375036*T - 4082762597251112041981011628045915169922015975371082484207702031580036343831192388289503810246561812442507631318438367983406039676
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