[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
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
\(2\)
\(1\)
\(3\)
\(-1\)
\(7\)
\(-1\)
\(13\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{5} + 340T_{5}^{4} - 97735T_{5}^{3} - 30126750T_{5}^{2} - 2005595100T_{5} - 20103633000 \)
T5^5 + 340*T5^4 - 97735*T5^3 - 30126750*T5^2 - 2005595100*T5 - 20103633000
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(546))\).
$p$
$F_p(T)$
$2$
\( (T + 8)^{5} \)
(T + 8)^5
$3$
\( (T - 27)^{5} \)
(T - 27)^5
$5$
\( T^{5} + 340 T^{4} + \cdots - 20103633000 \)
T^5 + 340*T^4 - 97735*T^3 - 30126750*T^2 - 2005595100*T - 20103633000
$7$
\( (T - 343)^{5} \)
(T - 343)^5
$11$
\( T^{5} + 1303 T^{4} + \cdots + 47\!\cdots\!04 \)
T^5 + 1303*T^4 - 55327618*T^3 - 126164977512*T^2 + 353916337614912*T + 472759058028177504
$13$
\( (T - 2197)^{5} \)
(T - 2197)^5
$17$
\( T^{5} + 4247 T^{4} + \cdots - 40\!\cdots\!84 \)
T^5 + 4247*T^4 - 438002818*T^3 + 1178443110732*T^2 + 11992463195101272*T - 40332956705849892384
$19$
\( T^{5} + 16984 T^{4} + \cdots + 15\!\cdots\!56 \)
T^5 + 16984*T^4 - 2889729133*T^3 - 36515968273244*T^2 + 1984144016501690128*T + 15480301342070882709056
$23$
\( T^{5} + 78072 T^{4} + \cdots - 39\!\cdots\!64 \)
T^5 + 78072*T^4 - 3451779413*T^3 - 412822777067508*T^2 - 9524971936250323488*T - 39205100317176446040864
$29$
\( T^{5} + 213142 T^{4} + \cdots + 68\!\cdots\!28 \)
T^5 + 213142*T^4 - 22024243957*T^3 - 5768015571958758*T^2 - 117083948314971354732*T + 6853819542306138381520728
$31$
\( T^{5} + 186027 T^{4} + \cdots + 31\!\cdots\!40 \)
T^5 + 186027*T^4 - 33934766976*T^3 - 5412265351896992*T^2 + 210457874211676811136*T + 31893695192544044788131840
$37$
\( T^{5} - 101025 T^{4} + \cdots - 92\!\cdots\!00 \)
T^5 - 101025*T^4 - 222188508590*T^3 + 28894910820168100*T^2 + 7777564118966557715400*T - 927857990593872891247976000
$41$
\( T^{5} + 23976 T^{4} + \cdots - 92\!\cdots\!00 \)
T^5 + 23976*T^4 - 428236884080*T^3 + 2410001635624560*T^2 + 22294433515472561653200*T - 923852905088527546065273600
$43$
\( T^{5} + 55528 T^{4} + \cdots - 13\!\cdots\!48 \)
T^5 + 55528*T^4 - 685178858837*T^3 + 81398594748079588*T^2 + 89139975724963847021968*T - 13999712064608320786307690048
$47$
\( T^{5} + 985981 T^{4} + \cdots + 81\!\cdots\!00 \)
T^5 + 985981*T^4 - 1256669183264*T^3 - 1373663362803969744*T^2 - 135476796044142838896624*T + 81578274654066539176436716800
$53$
\( T^{5} + 1891657 T^{4} + \cdots + 36\!\cdots\!00 \)
T^5 + 1891657*T^4 - 2774786348360*T^3 - 5856003863804457720*T^2 + 1199126546906708365477200*T + 3631446708521307784169802958800
$59$
\( T^{5} + 2802208 T^{4} + \cdots + 19\!\cdots\!44 \)
T^5 + 2802208*T^4 - 3674020647808*T^3 - 9232347605260851792*T^2 + 4267410701158668164092992*T + 1929870244244554233361342009344
$61$
\( T^{5} - 1140591 T^{4} + \cdots - 40\!\cdots\!00 \)
T^5 - 1140591*T^4 - 10781014404500*T^3 + 14326472252990949760*T^2 + 27998727799586629101163200*T - 40842699805612597251561860944400
$67$
\( T^{5} - 265168 T^{4} + \cdots + 42\!\cdots\!00 \)
T^5 - 265168*T^4 - 6062377254220*T^3 - 5150253795222589520*T^2 - 463089489196775516008000*T + 42103686671684698565173356800
$71$
\( T^{5} + 4483276 T^{4} + \cdots + 10\!\cdots\!32 \)
T^5 + 4483276*T^4 - 5701398079496*T^3 - 34492496878117683984*T^2 - 21769778382268442661824256*T + 10526792329553849243525189336832
$73$
\( T^{5} + 2350578 T^{4} + \cdots - 25\!\cdots\!60 \)
T^5 + 2350578*T^4 - 24083522996261*T^3 - 12748271846092850738*T^2 + 87448787558579920247332596*T - 25593818542592095123645941467960
$79$
\( T^{5} + 4079889 T^{4} + \cdots + 19\!\cdots\!00 \)
T^5 + 4079889*T^4 - 46094274278174*T^3 - 185983625351501379536*T^2 + 505512312467560467304982976*T + 1997915638533382510583672799788800
$83$
\( T^{5} + 8731571 T^{4} + \cdots + 65\!\cdots\!32 \)
T^5 + 8731571*T^4 - 29764324900846*T^3 - 361642835409558906744*T^2 - 643698568498037108258204496*T + 65803706965968018408979433579232
$89$
\( T^{5} + 20077879 T^{4} + \cdots + 19\!\cdots\!00 \)
T^5 + 20077879*T^4 + 145541767034120*T^3 + 460288912517558160240*T^2 + 585649101552813911991110400*T + 191492609459591265359446898247600
$97$
\( T^{5} - 3780209 T^{4} + \cdots - 19\!\cdots\!92 \)
T^5 - 3780209*T^4 - 402455205190672*T^3 + 1852043649965284318504*T^2 + 33237008413522728795686563312*T - 192222445502396166399588280093214992
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