[N,k,chi] = [1002,2,Mod(1,1002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1002.1");
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
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(167\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{7} - 5T_{5}^{6} - 11T_{5}^{5} + 93T_{5}^{4} - 110T_{5}^{3} - 110T_{5}^{2} + 208T_{5} - 64 \)
T5^7 - 5*T5^6 - 11*T5^5 + 93*T5^4 - 110*T5^3 - 110*T5^2 + 208*T5 - 64
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{7} \)
(T - 1)^7
$3$
\( (T - 1)^{7} \)
(T - 1)^7
$5$
\( T^{7} - 5 T^{6} - 11 T^{5} + 93 T^{4} + \cdots - 64 \)
T^7 - 5*T^6 - 11*T^5 + 93*T^4 - 110*T^3 - 110*T^2 + 208*T - 64
$7$
\( T^{7} - 7 T^{6} - 5 T^{5} + 99 T^{4} + \cdots + 576 \)
T^7 - 7*T^6 - 5*T^5 + 99*T^4 - 28*T^3 - 448*T^2 + 96*T + 576
$11$
\( T^{7} - 48 T^{5} + 12 T^{4} + \cdots + 1152 \)
T^7 - 48*T^5 + 12*T^4 + 624*T^3 - 368*T^2 - 1344*T + 1152
$13$
\( T^{7} - 6 T^{6} - 30 T^{5} + 244 T^{4} + \cdots - 384 \)
T^7 - 6*T^6 - 30*T^5 + 244*T^4 - 288*T^3 - 552*T^2 + 1088*T - 384
$17$
\( T^{7} - 6 T^{6} - 56 T^{5} + \cdots - 1808 \)
T^7 - 6*T^6 - 56*T^5 + 184*T^4 + 1108*T^3 - 160*T^2 - 2960*T - 1808
$19$
\( T^{7} + 2 T^{6} - 116 T^{5} + \cdots - 7808 \)
T^7 + 2*T^6 - 116*T^5 - 44*T^4 + 3936*T^3 - 3312*T^2 - 22912*T - 7808
$23$
\( T^{7} - 92 T^{5} - 140 T^{4} + \cdots + 1024 \)
T^7 - 92*T^5 - 140*T^4 + 1808*T^3 + 3296*T^2 - 4608*T + 1024
$29$
\( T^{7} + 4 T^{6} - 160 T^{5} + \cdots - 67328 \)
T^7 + 4*T^6 - 160*T^5 - 396*T^4 + 7936*T^3 + 9168*T^2 - 107904*T - 67328
$31$
\( T^{7} - 7 T^{6} - 69 T^{5} + \cdots - 17536 \)
T^7 - 7*T^6 - 69*T^5 + 371*T^4 + 1712*T^3 - 3608*T^2 - 19072*T - 17536
$37$
\( T^{7} + 3 T^{6} - 145 T^{5} + \cdots - 333456 \)
T^7 + 3*T^6 - 145*T^5 - 455*T^4 + 6552*T^3 + 21854*T^2 - 93904*T - 333456
$41$
\( T^{7} + 12 T^{6} - 104 T^{5} + \cdots - 171936 \)
T^7 + 12*T^6 - 104*T^5 - 1252*T^4 + 3124*T^3 + 34200*T^2 - 8208*T - 171936
$43$
\( T^{7} + 2 T^{6} - 134 T^{5} + \cdots + 125792 \)
T^7 + 2*T^6 - 134*T^5 + 144*T^4 + 4912*T^3 - 13032*T^2 - 38944*T + 125792
$47$
\( T^{7} + 11 T^{6} - 137 T^{5} + \cdots + 11184 \)
T^7 + 11*T^6 - 137*T^5 - 1255*T^4 + 3440*T^3 + 21648*T^2 + 28400*T + 11184
$53$
\( T^{7} - T^{6} - 101 T^{5} + 87 T^{4} + \cdots + 5072 \)
T^7 - T^6 - 101*T^5 + 87*T^4 + 2018*T^3 - 2330*T^2 - 4184*T + 5072
$59$
\( T^{7} + 19 T^{6} - 49 T^{5} + \cdots - 189800 \)
T^7 + 19*T^6 - 49*T^5 - 2059*T^4 - 712*T^3 + 55722*T^2 - 47560*T - 189800
$61$
\( T^{7} - 12 T^{6} - 132 T^{5} + \cdots - 2048 \)
T^7 - 12*T^6 - 132*T^5 + 1104*T^4 + 5984*T^3 - 9856*T^2 - 10752*T - 2048
$67$
\( T^{7} + 17 T^{6} - 371 T^{5} + \cdots - 17569912 \)
T^7 + 17*T^6 - 371*T^5 - 6697*T^4 + 34026*T^3 + 731998*T^2 - 150208*T - 17569912
$71$
\( T^{7} + 20 T^{6} + 32 T^{5} + \cdots - 2048 \)
T^7 + 20*T^6 + 32*T^5 - 1420*T^4 - 9536*T^3 - 20256*T^2 - 12800*T - 2048
$73$
\( T^{7} - 10 T^{6} - 180 T^{5} + \cdots - 395712 \)
T^7 - 10*T^6 - 180*T^5 + 1292*T^4 + 11680*T^3 - 31008*T^2 - 283392*T - 395712
$79$
\( T^{7} - 2 T^{6} - 260 T^{5} + \cdots - 502400 \)
T^7 - 2*T^6 - 260*T^5 + 276*T^4 + 20132*T^3 - 1024*T^2 - 392960*T - 502400
$83$
\( T^{7} + 7 T^{6} - 175 T^{5} + \cdots - 327912 \)
T^7 + 7*T^6 - 175*T^5 - 1321*T^4 + 6184*T^3 + 47694*T^2 - 48344*T - 327912
$89$
\( T^{7} + 3 T^{6} - 481 T^{5} + \cdots + 5628816 \)
T^7 + 3*T^6 - 481*T^5 - 39*T^4 + 62912*T^3 - 211096*T^2 - 1370480*T + 5628816
$97$
\( T^{7} + 3 T^{6} - 137 T^{5} + \cdots - 416 \)
T^7 + 3*T^6 - 137*T^5 + 177*T^4 + 1372*T^3 - 20*T^2 - 1168*T - 416
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