[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("165.1");
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
\(3\)
\(1\)
\(5\)
\(1\)
\(11\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{5} + T_{2}^{4} - 143T_{2}^{3} - 71T_{2}^{2} + 4216T_{2} + 3740 \)
T2^5 + T2^4 - 143*T2^3 - 71*T2^2 + 4216*T2 + 3740
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(165))\).
$p$
$F_p(T)$
$2$
\( T^{5} + T^{4} - 143 T^{3} - 71 T^{2} + \cdots + 3740 \)
T^5 + T^4 - 143*T^3 - 71*T^2 + 4216*T + 3740
$3$
\( (T + 9)^{5} \)
(T + 9)^5
$5$
\( (T + 25)^{5} \)
(T + 25)^5
$7$
\( T^{5} - 116 T^{4} + \cdots - 8452488256 \)
T^5 - 116*T^4 - 29240*T^3 + 2221728*T^2 + 219658640*T - 8452488256
$11$
\( (T + 121)^{5} \)
(T + 121)^5
$13$
\( T^{5} + 926 T^{4} + \cdots + 13445413206016 \)
T^5 + 926*T^4 - 333440*T^3 - 442235520*T^2 - 50135184384*T + 13445413206016
$17$
\( T^{5} + \cdots + 475773584554112 \)
T^5 + 246*T^4 - 5163312*T^3 - 901951040*T^2 + 6342725354304*T + 475773584554112
$19$
\( T^{5} - 3420 T^{4} + \cdots - 25\!\cdots\!92 \)
T^5 - 3420*T^4 - 6764448*T^3 + 31335996736*T^2 - 11595374722368*T - 25313552260072192
$23$
\( T^{5} + 4244 T^{4} + \cdots + 23\!\cdots\!04 \)
T^5 + 4244*T^4 - 22135392*T^3 - 113228427648*T^2 - 24959044848384*T + 233790348907234304
$29$
\( T^{5} + 2922 T^{4} + \cdots + 18\!\cdots\!88 \)
T^5 + 2922*T^4 - 56006552*T^3 - 71997461104*T^2 + 548574189958672*T + 181338381052515488
$31$
\( T^{5} + 6112 T^{4} + \cdots + 55\!\cdots\!00 \)
T^5 + 6112*T^4 - 88109312*T^3 - 448862224384*T^2 + 1099903063818240*T + 55315427386982400
$37$
\( T^{5} - 6654 T^{4} + \cdots - 11\!\cdots\!48 \)
T^5 - 6654*T^4 - 139548824*T^3 + 79427168912*T^2 + 2504775596522832*T - 1150992166986314848
$41$
\( T^{5} + 14934 T^{4} + \cdots - 86\!\cdots\!12 \)
T^5 + 14934*T^4 - 27138456*T^3 - 611142452624*T^2 + 1706447379011088*T - 866544624312164512
$43$
\( T^{5} - 10804 T^{4} + \cdots - 69\!\cdots\!08 \)
T^5 - 10804*T^4 - 241696312*T^3 + 2206183318176*T^2 + 9464642747581840*T - 69423958051999903808
$47$
\( T^{5} + 41460 T^{4} + \cdots - 59\!\cdots\!00 \)
T^5 + 41460*T^4 + 182839456*T^3 - 11296731320704*T^2 - 160266188660882176*T - 597870687859166387200
$53$
\( T^{5} + 62398 T^{4} + \cdots - 27\!\cdots\!48 \)
T^5 + 62398*T^4 + 1165254856*T^3 + 4163835135792*T^2 - 52594877378835760*T - 271045292765184703648
$59$
\( T^{5} - 8524 T^{4} + \cdots - 17\!\cdots\!20 \)
T^5 - 8524*T^4 - 1473812064*T^3 + 12094540558976*T^2 + 450640553935795456*T - 1759901705273728670720
$61$
\( T^{5} - 59010 T^{4} + \cdots + 27\!\cdots\!80 \)
T^5 - 59010*T^4 + 36120168*T^3 + 49161685445488*T^2 - 810150449523318448*T + 2743219954312312874080
$67$
\( T^{5} + 15772 T^{4} + \cdots - 76\!\cdots\!00 \)
T^5 + 15772*T^4 - 3016730048*T^3 - 14862808994304*T^2 + 305674137992573952*T - 762865433260107673600
$71$
\( T^{5} - 88124 T^{4} + \cdots - 45\!\cdots\!12 \)
T^5 - 88124*T^4 + 1035316672*T^3 + 46860914054656*T^2 - 229921440465198080*T - 4564113905730757414912
$73$
\( T^{5} + 118358 T^{4} + \cdots + 70\!\cdots\!96 \)
T^5 + 118358*T^4 - 1251848608*T^3 - 283706425347456*T^2 + 5420580622194073600*T + 7098786526476341149696
$79$
\( T^{5} - 57324 T^{4} + \cdots - 19\!\cdots\!84 \)
T^5 - 57324*T^4 - 4956260896*T^3 + 344154816877760*T^2 + 30449370427915968*T - 196719315406206728073984
$83$
\( T^{5} + 7268 T^{4} + \cdots + 58\!\cdots\!00 \)
T^5 + 7268*T^4 - 10375609064*T^3 - 545999970570496*T^2 - 7454387833664722160*T + 5846355088719392734400
$89$
\( T^{5} - 72978 T^{4} + \cdots + 35\!\cdots\!96 \)
T^5 - 72978*T^4 - 12359545848*T^3 + 1235828473960496*T^2 - 36652853042347298352*T + 356288459088400893568096
$97$
\( T^{5} + 59174 T^{4} + \cdots + 11\!\cdots\!12 \)
T^5 + 59174*T^4 - 22054172984*T^3 - 233035609258128*T^2 + 69554808317190886608*T + 1110176085252119613087712
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