[N,k,chi] = [2,44,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, 44, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 44);
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 \(\beta = 17280\sqrt{1589985537001}\).
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
\( p \)
Sign
\(2\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 22341634056T_{3} - 349979984298584645616 \)
T3^2 + 22341634056*T3 - 349979984298584645616
acting on \(S_{44}^{\mathrm{new}}(\Gamma_0(2))\).
$p$
$F_p(T)$
$2$
\( (T - 2097152)^{2} \)
(T - 2097152)^2
$3$
\( T^{2} + 22341634056 T - 34\!\cdots\!16 \)
T^2 + 22341634056*T - 349979984298584645616
$5$
\( T^{2} + 47320658398020 T - 17\!\cdots\!00 \)
T^2 + 47320658398020*T - 176432838298873588352978437500
$7$
\( T^{2} + \cdots - 36\!\cdots\!04 \)
T^2 + 222460131347038928*T - 3650735680539667185757769352202618304
$11$
\( T^{2} + \cdots + 28\!\cdots\!64 \)
T^2 + 41887858358166241718616*T + 285690253529662614500141373161811193582744464
$13$
\( T^{2} + \cdots + 56\!\cdots\!04 \)
T^2 + 1511213342321158511669396*T + 569267545113098105421047269902444136472534709604
$17$
\( T^{2} + \cdots - 90\!\cdots\!24 \)
T^2 + 67349878355730307414152348*T - 90217889977587143385813674254611795958256225296011324
$19$
\( T^{2} + \cdots + 37\!\cdots\!00 \)
T^2 - 1230904208507994915735409240*T + 378779549043537624118881256622873804448360539852890000
$23$
\( T^{2} + \cdots - 50\!\cdots\!56 \)
T^2 - 38167008283484201492558062224*T - 50123153174895412879141023877962183384308857189453138385856
$29$
\( T^{2} + \cdots + 10\!\cdots\!00 \)
T^2 + 72780948725084997011410245083700*T + 1066049948610791255578560734224706336735826794583554031266100900
$31$
\( T^{2} + \cdots - 14\!\cdots\!56 \)
T^2 - 40207733905312243999256937298624*T - 14451297927362170423766875070394347134333660122480746291752672256
$37$
\( T^{2} + \cdots - 40\!\cdots\!24 \)
T^2 - 3383801276601910515940174638928252*T - 40819645471496935567589728713431542144014776025443024512549365289724
$41$
\( T^{2} + \cdots + 35\!\cdots\!04 \)
T^2 + 58505417265395086228405561355069196*T + 354963508153408573900718874300746806959812525055561789903147872660004
$43$
\( T^{2} + \cdots + 18\!\cdots\!84 \)
T^2 + 285092737981269186332521030698108056*T + 18439238313015946004710883490638854254429163316057916479228126733207184
$47$
\( T^{2} + \cdots + 43\!\cdots\!96 \)
T^2 - 1834986318326201344851046619753827872*T + 436483010695849295603603422627980906227838233260707940850634256925450496
$53$
\( T^{2} + \cdots + 45\!\cdots\!24 \)
T^2 - 13488383575332508144313645312419699164*T + 45478026327907598447829628140680776747167915506203566111086078735401037124
$59$
\( T^{2} + \cdots - 16\!\cdots\!00 \)
T^2 - 6535875469255007418951566075676717000*T - 1633419518428443155579337122830212059145924158481741830853925856353088732400
$61$
\( T^{2} + \cdots - 13\!\cdots\!16 \)
T^2 - 84915949989376412900726656980650069644*T - 13790264244762565215700023329846325237412275216727177149923984257369488234716
$67$
\( T^{2} + \cdots + 36\!\cdots\!16 \)
T^2 + 3889814457887475263640354897004803753608*T + 3668548235882285827581881859853861667959350268168295478144606391207904560704016
$71$
\( T^{2} + \cdots - 72\!\cdots\!96 \)
T^2 + 4500205056814555193905197090502997775696*T - 72753551921208789745927780155583838209857779172090460293506089998003096911311296
$73$
\( T^{2} + \cdots - 64\!\cdots\!16 \)
T^2 + 10215757578580250274581767012298787143756*T - 64520553672133177335173771486607199748893344636719280535376515713066133921626716
$79$
\( T^{2} + \cdots + 27\!\cdots\!00 \)
T^2 - 106263833346898669088358572211107427639520*T + 2736666117955282434495057753882689443701149206312994955391256026958661519150035200
$83$
\( T^{2} + \cdots - 20\!\cdots\!16 \)
T^2 + 99535113533406416106304387849461181193256*T - 20785699434854541991433761329614954776981474261617071400919398723243846870267989616
$89$
\( T^{2} + \cdots - 18\!\cdots\!00 \)
T^2 - 175134609645798670638848613045046472300820*T - 186595774682821568193884097761833247658446172710754854041836771667020397798393791900
$97$
\( T^{2} + \cdots - 64\!\cdots\!64 \)
T^2 + 3659395264822684391406294706085506900627388*T - 64384534645616014624363300198936055541488712018581509691749009546065831944877057514364
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