[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
\( T_{5}^{5} + T_{5}^{4} - 19T_{5}^{3} - 21T_{5}^{2} + 60T_{5} + 24 \)
T5^5 + T5^4 - 19*T5^3 - 21*T5^2 + 60*T5 + 24
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{5} \)
(T + 1)^5
$3$
\( (T - 1)^{5} \)
(T - 1)^5
$5$
\( T^{5} + T^{4} - 19 T^{3} - 21 T^{2} + \cdots + 24 \)
T^5 + T^4 - 19*T^3 - 21*T^2 + 60*T + 24
$7$
\( T^{5} - 9 T^{4} + 15 T^{3} + 49 T^{2} + \cdots + 72 \)
T^5 - 9*T^4 + 15*T^3 + 49*T^2 - 132*T + 72
$11$
\( T^{5} + 2 T^{4} - 28 T^{3} - 60 T^{2} + \cdots + 288 \)
T^5 + 2*T^4 - 28*T^3 - 60*T^2 + 144*T + 288
$13$
\( T^{5} - 6 T^{4} - 2 T^{3} + 52 T^{2} + \cdots - 8 \)
T^5 - 6*T^4 - 2*T^3 + 52*T^2 - 48*T - 8
$17$
\( T^{5} - 4 T^{4} - 10 T^{3} + 24 T^{2} + \cdots - 24 \)
T^5 - 4*T^4 - 10*T^3 + 24*T^2 + 24*T - 24
$19$
\( T^{5} - 12 T^{4} + 28 T^{3} + \cdots - 176 \)
T^5 - 12*T^4 + 28*T^3 + 100*T^2 - 288*T - 176
$23$
\( T^{5} - 2 T^{4} - 28 T^{3} + 60 T^{2} + \cdots - 288 \)
T^5 - 2*T^4 - 28*T^3 + 60*T^2 + 144*T - 288
$29$
\( T^{5} + 6 T^{4} - 84 T^{3} + \cdots - 1728 \)
T^5 + 6*T^4 - 84*T^3 - 300*T^2 + 1728*T - 1728
$31$
\( T^{5} - 9 T^{4} - 5 T^{3} + 229 T^{2} + \cdots + 256 \)
T^5 - 9*T^4 - 5*T^3 + 229*T^2 - 576*T + 256
$37$
\( T^{5} - 5 T^{4} - 67 T^{3} + 415 T^{2} + \cdots - 226 \)
T^5 - 5*T^4 - 67*T^3 + 415*T^2 - 344*T - 226
$41$
\( T^{5} - 4 T^{4} - 110 T^{3} + \cdots + 4176 \)
T^5 - 4*T^4 - 110*T^3 - 132*T^2 + 1800*T + 4176
$43$
\( T^{5} - 18 T^{4} - 24 T^{3} + \cdots + 17424 \)
T^5 - 18*T^4 - 24*T^3 + 2044*T^2 - 11808*T + 17424
$47$
\( T^{5} + 7 T^{4} - 61 T^{3} - 243 T^{2} + \cdots - 156 \)
T^5 + 7*T^4 - 61*T^3 - 243*T^2 + 1104*T - 156
$53$
\( T^{5} - 3 T^{4} - 209 T^{3} + \cdots - 43392 \)
T^5 - 3*T^4 - 209*T^3 + 717*T^2 + 10608*T - 43392
$59$
\( T^{5} - 13 T^{4} - 127 T^{3} + \cdots - 3306 \)
T^5 - 13*T^4 - 127*T^3 + 2295*T^2 - 7092*T - 3306
$61$
\( T^{5} - 16 T^{4} - 28 T^{3} + \cdots - 14848 \)
T^5 - 16*T^4 - 28*T^3 + 1024*T^2 + 128*T - 14848
$67$
\( T^{5} - 9 T^{4} - 155 T^{3} + \cdots - 36476 \)
T^5 - 9*T^4 - 155*T^3 + 1585*T^2 + 2316*T - 36476
$71$
\( T^{5} + 10 T^{4} - 184 T^{3} + \cdots + 3456 \)
T^5 + 10*T^4 - 184*T^3 - 1476*T^2 + 4320*T + 3456
$73$
\( T^{5} - 8 T^{4} - 104 T^{3} + \cdots - 2768 \)
T^5 - 8*T^4 - 104*T^3 + 652*T^2 + 2128*T - 2768
$79$
\( T^{5} - 6 T^{4} - 102 T^{3} + \cdots - 6336 \)
T^5 - 6*T^4 - 102*T^3 + 808*T^2 - 96*T - 6336
$83$
\( T^{5} - T^{4} - 281 T^{3} + \cdots + 10266 \)
T^5 - T^4 - 281*T^3 + 165*T^2 + 16956*T + 10266
$89$
\( T^{5} + 5 T^{4} - 205 T^{3} + \cdots + 50268 \)
T^5 + 5*T^4 - 205*T^3 - 1137*T^2 + 8952*T + 50268
$97$
\( T^{5} + 7 T^{4} - 253 T^{3} + \cdots + 27848 \)
T^5 + 7*T^4 - 253*T^3 - 1835*T^2 + 5740*T + 27848
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