[N,k,chi] = [3,26,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 26);
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
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 3678T_{2}^{2} - 88941600T_{2} - 172099067904 \)
T2^3 + 3678*T2^2 - 88941600*T2 - 172099067904
acting on \(S_{26}^{\mathrm{new}}(\Gamma_0(3))\).
$p$
$F_p(T)$
$2$
\( T^{3} + 3678 T^{2} + \cdots - 172099067904 \)
T^3 + 3678*T^2 - 88941600*T - 172099067904
$3$
\( (T - 531441)^{3} \)
(T - 531441)^3
$5$
\( T^{3} + 163152750 T^{2} + \cdots + 28\!\cdots\!00 \)
T^3 + 163152750*T^2 - 576360839593732500*T + 28193553433383376919625000
$7$
\( T^{3} + 9622572744 T^{2} + \cdots - 45\!\cdots\!80 \)
T^3 + 9622572744*T^2 - 2735730288033009320256*T - 45496305709050204425120004385280
$11$
\( T^{3} + 5946998130780 T^{2} + \cdots - 18\!\cdots\!84 \)
T^3 + 5946998130780*T^2 - 241304384811119802301614672*T - 1804461232716966113502091608885829320384
$13$
\( T^{3} - 248137774407690 T^{2} + \cdots + 43\!\cdots\!48 \)
T^3 - 248137774407690*T^2 + 15042537196632170418319600332*T + 43166753830738834483986868858869452219848
$17$
\( T^{3} + \cdots - 75\!\cdots\!12 \)
T^3 - 6640885201245174*T^2 + 12708578979420482013432813746892*T - 7518940772597110273935376987539826401977005512
$19$
\( T^{3} + \cdots + 12\!\cdots\!00 \)
T^3 + 4282718959080516*T^2 - 60631496562957984335683530223440*T + 12162862331013788283671448662188371157932894400
$23$
\( T^{3} + \cdots + 17\!\cdots\!80 \)
T^3 + 54558955951564152*T^2 - 878929887412451777103154122087744*T + 170272476680992741279142033306638774933068986880
$29$
\( T^{3} + 506350856671782 T^{2} + \cdots + 69\!\cdots\!00 \)
T^3 + 506350856671782*T^2 - 7169030600757121136170698466824964980*T + 6971772888908511976696860780594808803482876251879153800
$31$
\( T^{3} + \cdots + 15\!\cdots\!00 \)
T^3 + 120595458951353856*T^2 - 17940046271689419137617753457621385216*T + 15367610460131749417073926115926266102329215465868492800
$37$
\( T^{3} + \cdots + 78\!\cdots\!60 \)
T^3 - 71124029266471833426*T^2 + 1044599360204826846189044112217470134124*T + 7811756720161662257189255190043447281866360536880266590760
$41$
\( T^{3} + \cdots - 20\!\cdots\!80 \)
T^3 + 178237898435247428226*T^2 - 30094451405602189199646420129066630719316*T - 2088539850446729617470260503625109533089647493337248415954280
$43$
\( T^{3} + \cdots + 18\!\cdots\!44 \)
T^3 - 233732145791955002244*T^2 - 301308621085438934235935311563132887376*T + 1886539054145254649255912388977295129031492931359941606900544
$47$
\( T^{3} + \cdots - 12\!\cdots\!28 \)
T^3 + 578974907441950806192*T^2 - 1993024637434206095515438676351440622333184*T - 1239589233623657381519877182901024729447078733720680258310729728
$53$
\( T^{3} + \cdots - 14\!\cdots\!80 \)
T^3 - 9056010625929165756258*T^2 + 23359816302444825754296879800736887227624236*T - 14969683185687662326810117064012267196735097723201794570335955480
$59$
\( T^{3} + \cdots - 28\!\cdots\!00 \)
T^3 - 23769324802557802948596*T^2 + 154389667234784180409487080809698573841252400*T - 287646445827220960940713003443277799009236064303740619165649240000
$61$
\( T^{3} + \cdots + 16\!\cdots\!48 \)
T^3 + 11371716695373075009318*T^2 - 497146146494865321601520770455978569046677364*T + 1698645814052553959684748531384679012020098528370313771328234099848
$67$
\( T^{3} + \cdots + 19\!\cdots\!88 \)
T^3 - 52213761253321486240524*T^2 - 5074580872411877364032098020617277352094509008*T + 192183633766761016150867178945973055523751179941223502434652273201088
$71$
\( T^{3} + \cdots - 19\!\cdots\!28 \)
T^3 - 262955361870665606618136*T^2 + 16981219910348982992999229299385984415528304832*T - 192159313060595077008327143774785111163215361088304037697071089648128
$73$
\( T^{3} + \cdots - 36\!\cdots\!00 \)
T^3 + 11752720924176446629602*T^2 - 61151088095231247609767712229230475709329050324*T - 3628636249115293430828207046339130950548444949081032830745187921741800
$79$
\( T^{3} + \cdots - 90\!\cdots\!00 \)
T^3 + 500543105756664483755760*T^2 - 220131581651028989960577499995102195867397305600*T - 90057478501151144703721781765161111216072496873915321069809800429056000
$83$
\( T^{3} + \cdots + 45\!\cdots\!72 \)
T^3 + 59055829437561671377284*T^2 - 1543799631617645025566564335335626916669552759120*T + 453052184280895293617957504006977697036214618101924299307884639388359872
$89$
\( T^{3} + \cdots - 44\!\cdots\!00 \)
T^3 + 3359875059386549548018866*T^2 - 2815954870029028645203670538954449999509026053140*T - 4489285186902748398377523940205847761533327967407097885326727945234706600
$97$
\( T^{3} + \cdots - 69\!\cdots\!52 \)
T^3 + 12029431225244267569541466*T^2 + 23151569584785666361042762512792746187604184499852*T - 69108744623418728986144107579535301336959662132620025552305977687823766152
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