[N,k,chi] = [456,6,Mod(1,456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(456, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("456.1");
S:= CuspForms(chi, 6);
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{6} + 65T_{5}^{5} - 9557T_{5}^{4} - 445577T_{5}^{3} + 29529208T_{5}^{2} + 602356212T_{5} - 26557430352 \)
T5^6 + 65*T5^5 - 9557*T5^4 - 445577*T5^3 + 29529208*T5^2 + 602356212*T5 - 26557430352
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(456))\).
$p$
$F_p(T)$
$2$
\( T^{6} \)
T^6
$3$
\( (T + 9)^{6} \)
(T + 9)^6
$5$
\( T^{6} + 65 T^{5} + \cdots - 26557430352 \)
T^6 + 65*T^5 - 9557*T^4 - 445577*T^3 + 29529208*T^2 + 602356212*T - 26557430352
$7$
\( T^{6} + 149 T^{5} + \cdots - 143821013760 \)
T^6 + 149*T^5 - 58601*T^4 - 7618369*T^3 + 616968276*T^2 + 47041668096*T - 143821013760
$11$
\( T^{6} + 203 T^{5} + \cdots + 1637954874112 \)
T^6 + 203*T^5 - 251657*T^4 + 17133601*T^3 + 4031719924*T^2 - 267853720384*T + 1637954874112
$13$
\( T^{6} + 298 T^{5} + \cdots - 67\!\cdots\!72 \)
T^6 + 298*T^5 - 1307040*T^4 - 343769584*T^3 + 264801371792*T^2 + 15213557591328*T - 6708606782009472
$17$
\( T^{6} - 1319 T^{5} + \cdots + 11\!\cdots\!20 \)
T^6 - 1319*T^5 - 4786951*T^4 + 4944257071*T^3 + 4545676438234*T^2 - 1696792136443948*T + 112483698699536520
$19$
\( (T - 361)^{6} \)
(T - 361)^6
$23$
\( T^{6} - 1234 T^{5} + \cdots + 10\!\cdots\!44 \)
T^6 - 1234*T^5 - 16647152*T^4 + 26840454464*T^3 + 26100108896512*T^2 - 45742188138549760*T + 10912197866748678144
$29$
\( T^{6} - 7356 T^{5} + \cdots + 86\!\cdots\!48 \)
T^6 - 7356*T^5 - 63158820*T^4 + 470208142688*T^3 + 247015746026736*T^2 - 5798286151586715072*T + 8642687692042412394048
$31$
\( T^{6} - 1632 T^{5} + \cdots + 17\!\cdots\!16 \)
T^6 - 1632*T^5 - 89208160*T^4 + 402954089040*T^3 - 151177840715920*T^2 - 21145538634270528*T + 1775258940705673216
$37$
\( T^{6} - 14204 T^{5} + \cdots + 44\!\cdots\!00 \)
T^6 - 14204*T^5 - 152187540*T^4 + 2549548661904*T^3 - 3937790841698560*T^2 - 21855154949371187200*T + 44634198355839424512000
$41$
\( T^{6} - 14734 T^{5} + \cdots + 13\!\cdots\!32 \)
T^6 - 14734*T^5 - 218995972*T^4 + 3521404106744*T^3 + 4295040987543424*T^2 - 137944351507367165952*T + 130014003424053810143232
$43$
\( T^{6} + 4693 T^{5} + \cdots - 77\!\cdots\!60 \)
T^6 + 4693*T^5 - 121424401*T^4 - 13046528417*T^3 + 2310347035035788*T^2 + 220901908593157840*T - 7782465890442830048960
$47$
\( T^{6} + 10955 T^{5} + \cdots + 60\!\cdots\!28 \)
T^6 + 10955*T^5 - 875485039*T^4 - 12059614729919*T^3 + 109163360832510938*T^2 + 1950611936993183535176*T + 6017573213501270549790528
$53$
\( T^{6} - 47500 T^{5} + \cdots + 85\!\cdots\!12 \)
T^6 - 47500*T^5 - 1362911364*T^4 + 76411039032672*T^3 - 27461508012574992*T^2 - 16841270001755946651840*T + 85877369677236344214606912
$59$
\( T^{6} + 61744 T^{5} + \cdots - 49\!\cdots\!12 \)
T^6 + 61744*T^5 - 523832560*T^4 - 107702950243712*T^3 - 2508318902055701248*T^2 - 19827079600836999059456*T - 49458837070203928468877312
$61$
\( T^{6} + 81581 T^{5} + \cdots + 42\!\cdots\!00 \)
T^6 + 81581*T^5 - 1397314919*T^4 - 214064110340925*T^3 - 2680188236475503230*T^2 + 31773398360921964208564*T + 422387419150841053436073800
$67$
\( T^{6} + 45756 T^{5} + \cdots + 85\!\cdots\!76 \)
T^6 + 45756*T^5 - 2579706560*T^4 - 112565725121280*T^3 + 405388370893277440*T^2 + 19742234648201362707456*T + 85818577087046686638514176
$71$
\( T^{6} + 10416 T^{5} + \cdots + 11\!\cdots\!80 \)
T^6 + 10416*T^5 - 7810260288*T^4 - 91249375845248*T^3 + 12054624853039017984*T^2 + 241427407200421726126080*T + 1178294627230390149426708480
$73$
\( T^{6} + 54615 T^{5} + \cdots + 21\!\cdots\!08 \)
T^6 + 54615*T^5 - 4851012187*T^4 - 249447316672487*T^3 + 3166952202416264678*T^2 + 238642259644454485822572*T + 2133080321332010228647838808
$79$
\( T^{6} + 145594 T^{5} + \cdots + 13\!\cdots\!88 \)
T^6 + 145594*T^5 + 6759148176*T^4 + 91150843755968*T^3 - 565134851002588160*T^2 - 7998241529329578250752*T + 1327446078105548791410688
$83$
\( T^{6} + 160548 T^{5} + \cdots + 12\!\cdots\!00 \)
T^6 + 160548*T^5 + 1059380944*T^4 - 896709308291392*T^3 - 42414970839760802304*T^2 - 187835742431011107184640*T + 12305956014840693565417062400
$89$
\( T^{6} + 97728 T^{5} + \cdots + 37\!\cdots\!84 \)
T^6 + 97728*T^5 - 18458090156*T^4 - 1821987516761856*T^3 + 28929446906634701616*T^2 + 3068595899308725295915008*T + 37534826904015805011082689984
$97$
\( T^{6} + 760 T^{5} + \cdots - 53\!\cdots\!24 \)
T^6 + 760*T^5 - 14254958316*T^4 - 3353906992256*T^3 + 55323449017729409200*T^2 - 188878259306695067372928*T - 53938708072719757126852981824
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