[N,k,chi] = [24,22,Mod(1,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.1");
S:= CuspForms(chi, 22);
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
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
\(2\)
\(1\)
\(3\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 2080026T_{5}^{2} - 1387114113501300T_{5} - 11485065000261414395000 \)
T5^3 - 2080026*T5^2 - 1387114113501300*T5 - 11485065000261414395000
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(24))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( (T + 59049)^{3} \)
(T + 59049)^3
$5$
\( T^{3} - 2080026 T^{2} + \cdots - 11\!\cdots\!00 \)
T^3 - 2080026*T^2 - 1387114113501300*T - 11485065000261414395000
$7$
\( T^{3} + 1205282064 T^{2} + \cdots - 44\!\cdots\!00 \)
T^3 + 1205282064*T^2 - 294077320947922176*T - 446714683228076576437555200
$11$
\( T^{3} - 13839247500 T^{2} + \cdots + 32\!\cdots\!16 \)
T^3 - 13839247500*T^2 - 21996460436355589340112*T + 32993936591098245846539449825216
$13$
\( T^{3} - 718855551690 T^{2} + \cdots + 76\!\cdots\!16 \)
T^3 - 718855551690*T^2 + 79803467605936924702668*T + 763049580012387144198574680009416
$17$
\( T^{3} - 2135189843046 T^{2} + \cdots + 14\!\cdots\!56 \)
T^3 - 2135189843046*T^2 - 92832491329608404235666036*T + 149675519499307887313555770421934798456
$19$
\( T^{3} + 40122324686988 T^{2} + \cdots - 15\!\cdots\!44 \)
T^3 + 40122324686988*T^2 - 132674035720995241142811600*T - 1554875472933386934158570282960006903744
$23$
\( T^{3} - 278424417682632 T^{2} + \cdots + 55\!\cdots\!00 \)
T^3 - 278424417682632*T^2 - 32343312198024407422734721344*T + 5556463927213384242376965204337585314572800
$29$
\( T^{3} - 442708167991794 T^{2} + \cdots + 22\!\cdots\!08 \)
T^3 - 442708167991794*T^2 - 2811701011742987310870590733588*T + 2290456793028600232891065482159085350153860008
$31$
\( T^{3} + \cdots + 46\!\cdots\!00 \)
T^3 - 8016070162990152*T^2 + 4382720251380096220801623049920*T + 46586908897908439106549929691788608594716838400
$37$
\( T^{3} + \cdots + 27\!\cdots\!00 \)
T^3 - 27729341388737058*T^2 - 1247771948343734882461091678526420*T + 27177097675803649720401639810650935363444009722600
$41$
\( T^{3} + \cdots - 32\!\cdots\!96 \)
T^3 + 125648125186340562*T^2 - 727439603509818180013815397432980*T - 320719352062144043428356299023445494690379086048296
$43$
\( T^{3} + \cdots - 17\!\cdots\!28 \)
T^3 + 229052541499074612*T^2 - 8836110641574057776540312446996944*T - 1762910840408642354529087333543391070036811347672128
$47$
\( T^{3} + \cdots - 36\!\cdots\!00 \)
T^3 + 448613782068047712*T^2 - 48014802699441032990402515107394560*T - 3691710422872482388768655619052549167571882133913600
$53$
\( T^{3} + \cdots + 64\!\cdots\!00 \)
T^3 - 1406206217208267066*T^2 - 5343401487329663463288467143847761140*T + 6446942660908930244395933843037096823815631530241973000
$59$
\( T^{3} + \cdots - 63\!\cdots\!32 \)
T^3 + 1844638981471622100*T^2 - 25733330133731446933568707227177382608*T - 6301894506885465023602146317179409301172287869439636032
$61$
\( T^{3} + \cdots + 90\!\cdots\!44 \)
T^3 + 3294066300350351382*T^2 - 23391636243497270677125833124101698740*T + 9014097793074103839221630988288849247766744755830236744
$67$
\( T^{3} + \cdots - 55\!\cdots\!36 \)
T^3 + 33491023693155020652*T^2 - 3339141441357207810350097947428370640*T - 5518649314501573880392076747880531550075421294205526694336
$71$
\( T^{3} + \cdots - 11\!\cdots\!48 \)
T^3 + 79431018431598881160*T^2 + 1574149239269019090393435529866545656512*T - 114697967065289083531311033263463099653581393265643125248
$73$
\( T^{3} + \cdots - 43\!\cdots\!84 \)
T^3 + 46612822906958319618*T^2 - 963003731556909563732231124429293131092*T - 43603280660451355429737419168989661812094048948255345012584
$79$
\( T^{3} + \cdots - 74\!\cdots\!88 \)
T^3 + 197919973704661098024*T^2 + 6822238093444863217801798215046240128192*T - 74272191336148085472266841305472518520836501545126789247488
$83$
\( T^{3} + \cdots + 62\!\cdots\!32 \)
T^3 - 111848528551886940276*T^2 - 64348028853504883554429607906510950663120*T + 6224089420162930059494601935929235265786053173564336430676032
$89$
\( T^{3} + \cdots + 55\!\cdots\!40 \)
T^3 + 731008175840243483058*T^2 + 137338336518055316110446765527283784196076*T + 5553249736449635731810798705236831349560798424935150037828440
$97$
\( T^{3} + \cdots - 12\!\cdots\!88 \)
T^3 + 1594521920055126193722*T^2 + 480169996404493000524099602416002569328396*T - 129011563726709146581946221656537643634509941801594440613594888
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