[N,k,chi] = [5292,2,Mod(361,5292)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5292, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5292.361");
S:= CuspForms(chi, 2);
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 \(\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times\).
\(n\)
\(785\)
\(1081\)
\(2647\)
\(\chi(n)\)
\(-1 + \beta_{1}\)
\(-\beta_{1}\)
\(1\)
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
\( T_{5}^{7} - 2T_{5}^{6} - 20T_{5}^{5} + 12T_{5}^{4} + 129T_{5}^{3} + 81T_{5}^{2} - 108T_{5} - 81 \)
T5^7 - 2*T5^6 - 20*T5^5 + 12*T5^4 + 129*T5^3 + 81*T5^2 - 108*T5 - 81
acting on \(S_{2}^{\mathrm{new}}(5292, [\chi])\).
$p$
$F_p(T)$
$2$
\( T^{14} \)
T^14
$3$
\( T^{14} \)
T^14
$5$
\( (T^{7} - 2 T^{6} - 20 T^{5} + 12 T^{4} + \cdots - 81)^{2} \)
(T^7 - 2*T^6 - 20*T^5 + 12*T^4 + 129*T^3 + 81*T^2 - 108*T - 81)^2
$7$
\( T^{14} \)
T^14
$11$
\( (T^{7} - 2 T^{6} - 41 T^{5} + 75 T^{4} + \cdots - 81)^{2} \)
(T^7 - 2*T^6 - 41*T^5 + 75*T^4 + 174*T^3 - 72*T^2 - 216*T - 81)^2
$13$
\( T^{14} + 2 T^{13} + 66 T^{12} + \cdots + 150626529 \)
T^14 + 2*T^13 + 66*T^12 + 150*T^11 + 3006*T^10 + 6792*T^9 + 72459*T^8 + 166125*T^7 + 1261032*T^6 + 2477084*T^5 + 11286787*T^4 + 13891926*T^3 + 57525819*T^2 + 59904513*T + 150626529
$17$
\( T^{14} - 2 T^{13} + 54 T^{12} + \cdots + 6561 \)
T^14 - 2*T^13 + 54*T^12 + 40*T^11 + 2053*T^10 + 717*T^9 + 25764*T^8 + 35055*T^7 + 229455*T^6 + 117693*T^5 + 252315*T^4 - 163782*T^3 + 171315*T^2 - 34992*T + 6561
$19$
\( T^{14} + 7 T^{13} + 79 T^{12} + \cdots + 4084441 \)
T^14 + 7*T^13 + 79*T^12 + 284*T^11 + 2483*T^10 + 7631*T^9 + 52224*T^8 + 107232*T^7 + 592827*T^6 + 1055750*T^5 + 4434668*T^4 + 3636557*T^3 + 6386590*T^2 - 2718245*T + 4084441
$23$
\( (T^{7} - 11 T^{6} - 32 T^{5} + 642 T^{4} + \cdots - 10287)^{2} \)
(T^7 - 11*T^6 - 32*T^5 + 642*T^4 - 825*T^3 - 7470*T^2 + 17928*T - 10287)^2
$29$
\( T^{14} + T^{13} + 114 T^{12} + \cdots + 145660761 \)
T^14 + T^13 + 114*T^12 - 461*T^11 + 9532*T^10 - 35634*T^9 + 388671*T^8 - 1678950*T^7 + 11256606*T^6 - 31944915*T^5 + 91122165*T^4 - 85897584*T^3 + 120307599*T^2 + 14663835*T + 145660761
$31$
\( T^{14} - T^{13} + 132 T^{12} + \cdots + 13807190016 \)
T^14 - T^13 + 132*T^12 + 147*T^11 + 12150*T^10 + 16791*T^9 + 545994*T^8 + 1403166*T^7 + 17765313*T^6 + 43173635*T^5 + 320145937*T^4 + 845293824*T^3 + 3991880448*T^2 + 6768230400*T + 13807190016
$37$
\( T^{14} - 10 T^{13} + \cdots + 1566893056 \)
T^14 - 10*T^13 + 175*T^12 - 554*T^11 + 9977*T^10 - 15644*T^9 + 457224*T^8 + 84720*T^7 + 9392352*T^6 - 5679392*T^5 + 108195008*T^4 - 22905344*T^3 + 616635136*T^2 - 582676480*T + 1566893056
$41$
\( T^{14} + 33 T^{13} + \cdots + 1108290681 \)
T^14 + 33*T^13 + 750*T^12 + 10647*T^11 + 122094*T^10 + 1058184*T^9 + 8343351*T^8 + 54852066*T^7 + 339156396*T^6 + 1620277101*T^5 + 6482676969*T^4 + 15810186042*T^3 + 27318068505*T^2 - 5174719749*T + 1108290681
$43$
\( T^{14} - 7 T^{13} + 79 T^{12} + \cdots + 4084441 \)
T^14 - 7*T^13 + 79*T^12 - 284*T^11 + 2483*T^10 - 7631*T^9 + 52224*T^8 - 107232*T^7 + 592827*T^6 - 1055750*T^5 + 4434668*T^4 - 3636557*T^3 + 6386590*T^2 + 2718245*T + 4084441
$47$
\( T^{14} + 3 T^{13} + 114 T^{12} + \cdots + 136048896 \)
T^14 + 3*T^13 + 114*T^12 - 45*T^11 + 8298*T^10 - 5832*T^9 + 323514*T^8 - 707130*T^7 + 8286543*T^6 - 8704260*T^5 + 45671121*T^4 - 56529576*T^3 + 199349424*T^2 - 158723712*T + 136048896
$53$
\( T^{14} - 15 T^{13} + \cdots + 952401321 \)
T^14 - 15*T^13 + 327*T^12 - 2412*T^11 + 43173*T^10 - 325539*T^9 + 3279960*T^8 - 13241718*T^7 + 74649195*T^6 - 196816392*T^5 + 1102507524*T^4 - 2291724495*T^3 + 4569369084*T^2 - 2277264051*T + 952401321
$59$
\( T^{14} + 14 T^{13} + \cdots + 688747536 \)
T^14 + 14*T^13 + 372*T^12 + 2198*T^11 + 56104*T^10 + 268263*T^9 + 5415255*T^8 + 3780486*T^7 + 180648873*T^6 - 380889378*T^5 + 6031230597*T^4 - 12726712872*T^3 + 38828496636*T^2 + 5050815264*T + 688747536
$61$
\( T^{14} - 10 T^{13} + \cdots + 148644864 \)
T^14 - 10*T^13 + 150*T^12 - 858*T^11 + 9648*T^10 - 50853*T^9 + 390015*T^8 - 1451094*T^7 + 8095101*T^6 - 25984822*T^5 + 111134833*T^4 - 224556408*T^3 + 371924448*T^2 - 270077184*T + 148644864
$67$
\( T^{14} - 6 T^{13} + 161 T^{12} + \cdots + 116985856 \)
T^14 - 6*T^13 + 161*T^12 - 1846*T^11 + 27063*T^10 - 205403*T^9 + 1253364*T^8 - 4649550*T^7 + 13920486*T^6 - 28174094*T^5 + 52651377*T^4 - 72186592*T^3 + 116493248*T^2 - 113178624*T + 116985856
$71$
\( (T^{7} + T^{6} - 116 T^{5} - 9 T^{4} + \cdots + 972)^{2} \)
(T^7 + T^6 - 116*T^5 - 9*T^4 + 2169*T^3 - 4509*T^2 + 1620*T + 972)^2
$73$
\( T^{14} + 21 T^{13} + \cdots + 2748590329 \)
T^14 + 21*T^13 + 404*T^12 + 3133*T^11 + 28230*T^10 + 68306*T^9 + 983931*T^8 + 713634*T^7 + 29169996*T^6 - 56145421*T^5 + 449343003*T^4 - 280079096*T^3 + 1197851843*T^2 + 132587883*T + 2748590329
$79$
\( T^{14} + 10 T^{13} + \cdots + 54397165824 \)
T^14 + 10*T^13 + 327*T^12 - 330*T^11 + 43659*T^10 - 155913*T^9 + 4930128*T^8 - 29255790*T^7 + 261464838*T^6 - 725781614*T^5 + 2999269969*T^4 - 5154931992*T^3 + 20914155312*T^2 - 28709926272*T + 54397165824
$83$
\( T^{14} + 25 T^{13} + \cdots + 901054679121 \)
T^14 + 25*T^13 + 738*T^12 + 9625*T^11 + 196147*T^10 + 2232114*T^9 + 33382563*T^8 + 219863025*T^7 + 1673845947*T^6 + 4248171090*T^5 + 31939205499*T^4 + 38563914105*T^3 + 552490013322*T^2 - 614158582239*T + 901054679121
$89$
\( T^{14} + 6 T^{13} + \cdots + 16524331209 \)
T^14 + 6*T^13 + 228*T^12 + 900*T^11 + 34641*T^10 + 125469*T^9 + 2286090*T^8 + 1816587*T^7 + 79129143*T^6 + 61446195*T^5 + 1553505561*T^4 - 765782424*T^3 + 13851839079*T^2 + 12932085294*T + 16524331209
$97$
\( T^{14} - 18 T^{13} + \cdots + 767677849 \)
T^14 - 18*T^13 + 347*T^12 - 1448*T^11 + 15987*T^10 + 13043*T^9 + 601413*T^8 + 1272273*T^7 + 13339572*T^6 + 52605197*T^5 + 225655953*T^4 + 522939832*T^3 + 992279576*T^2 + 1012081296*T + 767677849
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