[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4004.1");
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
\(2\)
\(-1\)
\(7\)
\(-1\)
\(11\)
\(-1\)
\(13\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} + 3T_{3}^{3} - 2T_{3}^{2} - 6T_{3} + 3 \)
T3^4 + 3*T3^3 - 2*T3^2 - 6*T3 + 3
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4004))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} + 3 T^{3} - 2 T^{2} - 6 T + 3 \)
T^4 + 3*T^3 - 2*T^2 - 6*T + 3
$5$
\( T^{4} + T^{3} - 8 T^{2} + 6 T - 1 \)
T^4 + T^3 - 8*T^2 + 6*T - 1
$7$
\( (T - 1)^{4} \)
(T - 1)^4
$11$
\( (T - 1)^{4} \)
(T - 1)^4
$13$
\( (T - 1)^{4} \)
(T - 1)^4
$17$
\( T^{4} + 7 T^{3} + 10 T^{2} - 18 T - 37 \)
T^4 + 7*T^3 + 10*T^2 - 18*T - 37
$19$
\( T^{4} + 9 T^{3} + 22 T^{2} + 12 T + 1 \)
T^4 + 9*T^3 + 22*T^2 + 12*T + 1
$23$
\( T^{4} - 3 T^{3} - 56 T^{2} + 252 T - 135 \)
T^4 - 3*T^3 - 56*T^2 + 252*T - 135
$29$
\( T^{4} + 3 T^{3} - 32 T^{2} - 24 T + 201 \)
T^4 + 3*T^3 - 32*T^2 - 24*T + 201
$31$
\( T^{4} - 22 T^{2} + 32 T + 5 \)
T^4 - 22*T^2 + 32*T + 5
$37$
\( T^{4} + 18 T^{3} + 72 T^{2} + \cdots - 1053 \)
T^4 + 18*T^3 + 72*T^2 - 189*T - 1053
$41$
\( T^{4} + 14 T^{3} + 8 T^{2} - 271 T + 379 \)
T^4 + 14*T^3 + 8*T^2 - 271*T + 379
$43$
\( T^{4} + T^{3} - 63 T^{2} - 197 T + 1 \)
T^4 + T^3 - 63*T^2 - 197*T + 1
$47$
\( T^{4} + 3 T^{3} - 72 T^{2} + 729 \)
T^4 + 3*T^3 - 72*T^2 + 729
$53$
\( T^{4} - 4 T^{3} - 53 T^{2} + 210 T - 117 \)
T^4 - 4*T^3 - 53*T^2 + 210*T - 117
$59$
\( T^{4} + 7 T^{3} - 19 T^{2} + T + 1 \)
T^4 + 7*T^3 - 19*T^2 + T + 1
$61$
\( T^{4} + 14 T^{3} - 44 T^{2} + \cdots - 139 \)
T^4 + 14*T^3 - 44*T^2 - 837*T - 139
$67$
\( T^{4} - 50 T^{2} + 96 T + 1 \)
T^4 - 50*T^2 + 96*T + 1
$71$
\( T^{4} - 88 T^{2} - 256 T + 80 \)
T^4 - 88*T^2 - 256*T + 80
$73$
\( T^{4} + 6 T^{3} - 166 T^{2} + \cdots + 1115 \)
T^4 + 6*T^3 - 166*T^2 - 437*T + 1115
$79$
\( T^{4} - 7 T^{3} - 149 T^{2} + \cdots + 2099 \)
T^4 - 7*T^3 - 149*T^2 + 633*T + 2099
$83$
\( T^{4} - 8 T^{3} - 166 T^{2} + \cdots + 3769 \)
T^4 - 8*T^3 - 166*T^2 + 865*T + 3769
$89$
\( T^{4} - 9 T^{3} - 160 T^{2} + \cdots + 2087 \)
T^4 - 9*T^3 - 160*T^2 + 346*T + 2087
$97$
\( T^{4} + 16 T^{3} + 50 T^{2} - 45 T - 27 \)
T^4 + 16*T^3 + 50*T^2 - 45*T - 27
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