[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8020.1");
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\).
We also show the integral \(q\)-expansion of the trace form .
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
\(2\)
\(-1\)
\(5\)
\(1\)
\(401\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 2T_{3} - 2 \)
T3^2 + 2*T3 - 2
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8020))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 2T - 2 \)
T^2 + 2*T - 2
$5$
\( (T + 1)^{2} \)
(T + 1)^2
$7$
\( T^{2} - 12 \)
T^2 - 12
$11$
\( T^{2} - 12 \)
T^2 - 12
$13$
\( T^{2} + 10T + 22 \)
T^2 + 10*T + 22
$17$
\( T^{2} - 2T - 2 \)
T^2 - 2*T - 2
$19$
\( T^{2} - 48 \)
T^2 - 48
$23$
\( T^{2} - 6T - 18 \)
T^2 - 6*T - 18
$29$
\( T^{2} - 4T - 8 \)
T^2 - 4*T - 8
$31$
\( T^{2} + 4T - 8 \)
T^2 + 4*T - 8
$37$
\( T^{2} - 10T - 2 \)
T^2 - 10*T - 2
$41$
\( T^{2} + 4T - 104 \)
T^2 + 4*T - 104
$43$
\( (T + 2)^{2} \)
(T + 2)^2
$47$
\( T^{2} + 4T - 44 \)
T^2 + 4*T - 44
$53$
\( T^{2} - 14T + 22 \)
T^2 - 14*T + 22
$59$
\( (T + 8)^{2} \)
(T + 8)^2
$61$
\( T^{2} - 4T - 44 \)
T^2 - 4*T - 44
$67$
\( T^{2} + 6T - 18 \)
T^2 + 6*T - 18
$71$
\( T^{2} - 12T + 24 \)
T^2 - 12*T + 24
$73$
\( T^{2} - 12T - 12 \)
T^2 - 12*T - 12
$79$
\( T^{2} \)
T^2
$83$
\( T^{2} + 4T - 188 \)
T^2 + 4*T - 188
$89$
\( T^{2} + 4T - 188 \)
T^2 + 4*T - 188
$97$
\( T^{2} - 18T + 78 \)
T^2 - 18*T + 78
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