[N,k,chi] = [98,10,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 10);
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
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\)
\(3\)
\(\chi(n)\)
\(-1 + \beta_{1}\)
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 subspace can be constructed as the kernel of the linear operator
\( T_{3}^{8} + 47322T_{3}^{6} + 1851596820T_{3}^{4} + 18350282114208T_{3}^{2} + 150369345150218496 \)
T3^8 + 47322*T3^6 + 1851596820*T3^4 + 18350282114208*T3^2 + 150369345150218496
acting on \(S_{10}^{\mathrm{new}}(98, [\chi])\).
$p$
$F_p(T)$
$2$
\( (T^{2} - 16 T + 256)^{4} \)
(T^2 - 16*T + 256)^4
$3$
\( T^{8} + 47322 T^{6} + \cdots + 15\!\cdots\!96 \)
T^8 + 47322*T^6 + 1851596820*T^4 + 18350282114208*T^2 + 150369345150218496
$5$
\( T^{8} + 4389322 T^{6} + \cdots + 24\!\cdots\!16 \)
T^8 + 4389322*T^6 + 19261196527188*T^4 + 21731939216727712*T^2 + 24513316903947510016
$7$
\( T^{8} \)
T^8
$11$
\( (T^{4} + 4774 T^{3} + \cdots + 84\!\cdots\!76)^{2} \)
(T^4 + 4774*T^3 + 2925255900*T^2 - 13856367069776*T + 8424302054557350976)^2
$13$
\( (T^{4} - 28441135314 T^{2} + \cdots + 20\!\cdots\!96)^{2} \)
(T^4 - 28441135314*T^2 + 200311573853265002496)^2
$17$
\( T^{8} + 364177565476 T^{6} + \cdots + 10\!\cdots\!76 \)
T^8 + 364177565476*T^6 + 100432901636705262276300*T^4 + 11723748969989047830679950257151376*T^2 + 1036350460617376988710311667493628523566236176
$19$
\( T^{8} + 760834631722 T^{6} + \cdots + 18\!\cdots\!36 \)
T^8 + 760834631722*T^6 + 536281867461913917526740*T^4 + 32402021570776727113981586473732768*T^2 + 1813692546969108366597759059988649087824199936
$23$
\( (T^{4} - 1418368 T^{3} + \cdots + 26\!\cdots\!04)^{2} \)
(T^4 - 1418368*T^3 + 2526075196176*T^2 + 729477176410228736*T + 264512114811656092213504)^2
$29$
\( (T^{2} - 8334986 T + 14857994423056)^{4} \)
(T^2 - 8334986*T + 14857994423056)^4
$31$
\( T^{8} + 74580188894856 T^{6} + \cdots + 16\!\cdots\!56 \)
T^8 + 74580188894856*T^6 + 4262661615215042532655474752*T^4 + 96920159461923852271182530935722086498304*T^2 + 1688811905866351867509581823219206373560495534826848256
$37$
\( (T^{4} + 1613186 T^{3} + \cdots + 29\!\cdots\!84)^{2} \)
(T^4 + 1613186*T^3 + 174823754883924*T^2 - 277825128494659343008*T + 29660205731463174900062435584)^2
$41$
\( (T^{4} - 524653229945812 T^{2} + \cdots + 15\!\cdots\!36)^{2} \)
(T^4 - 524653229945812*T^2 + 15175127626684854411860233636)^2
$43$
\( (T^{2} + 38240102 T + 187841499446728)^{4} \)
(T^2 + 38240102*T + 187841499446728)^4
$47$
\( T^{8} + \cdots + 70\!\cdots\!36 \)
T^8 + 2630861410847464*T^6 + 6894920910567866898496749291840*T^4 + 69746378859437022624359889517523629315139584*T^2 + 702825301254575649077781508310621872628632761764177575936
$53$
\( (T^{4} + 6854056 T^{3} + \cdots + 51\!\cdots\!44)^{2} \)
(T^4 + 6854056*T^3 + 7237167741483924*T^2 - 49281962565406767588128*T + 51698827315605584977840967852944)^2
$59$
\( T^{8} + \cdots + 14\!\cdots\!76 \)
T^8 + 6371386772799514*T^6 + 39385669354464980366800327879572*T^4 + 7702369814581826047235644852211036678799480736*T^2 + 1461439340898789380609389208292085858943569986464136959877376
$61$
\( T^{8} + \cdots + 61\!\cdots\!16 \)
T^8 + 13170727678904314*T^6 + 170995159483401805741889961546900*T^4 + 32569999271407445912219178258401998192635984544*T^2 + 6115274512859581867778553765526234650108666095126005087580416
$67$
\( (T^{4} - 407210388 T^{3} + \cdots + 96\!\cdots\!36)^{2} \)
(T^4 - 407210388*T^3 + 134746343393101200*T^2 - 12653637965320425349865472*T + 965590785118351426906847063310336)^2
$71$
\( (T^{2} + 662334372 T + 10\!\cdots\!64)^{4} \)
(T^2 + 662334372*T + 107691169551243264)^4
$73$
\( T^{8} + \cdots + 20\!\cdots\!76 \)
T^8 + 201160054502509972*T^6 + 40009358685014631794489833140529260*T^4 + 91730763598484869904572690687131173697910995717328*T^2 + 207944064381782118147115031484283011678031805987297221956140002576
$79$
\( (T^{4} - 334205588 T^{3} + \cdots + 59\!\cdots\!24)^{2} \)
(T^4 - 334205588*T^3 + 87312811133521776*T^2 - 8148120699620473764973184*T + 594411896906239754260854534145024)^2
$83$
\( (T^{4} + \cdots + 89\!\cdots\!96)^{2} \)
(T^4 - 280763948299304794*T^2 + 894141955513567640954711799502096)^2
$89$
\( T^{8} + \cdots + 37\!\cdots\!56 \)
T^8 + 989995707342536644*T^6 + 785802065519277132100686173460435852*T^4 + 192345706669005243408789644585424116093349594649217296*T^2 + 37748384567141323196114080850535342972689312718405288569636943224509456
$97$
\( (T^{4} + \cdots + 62\!\cdots\!56)^{2} \)
(T^4 - 1576090761528077764*T^2 + 620580982568256012338762988410362756)^2
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