[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
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 \(\beta = \frac{1}{2}(1 + \sqrt{5})\).
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
\(2\)
\(1\)
\(19\)
\(-1\)
\(211\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 3T_{3} + 1 \)
T3^2 - 3*T3 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{2} \)
(T + 1)^2
$3$
\( T^{2} - 3T + 1 \)
T^2 - 3*T + 1
$5$
\( T^{2} - 5 \)
T^2 - 5
$7$
\( (T - 2)^{2} \)
(T - 2)^2
$11$
\( T^{2} + 9T + 19 \)
T^2 + 9*T + 19
$13$
\( (T - 5)^{2} \)
(T - 5)^2
$17$
\( T^{2} - 5 \)
T^2 - 5
$19$
\( (T - 1)^{2} \)
(T - 1)^2
$23$
\( T^{2} + 12T + 31 \)
T^2 + 12*T + 31
$29$
\( T^{2} + 3T - 9 \)
T^2 + 3*T - 9
$31$
\( T^{2} - T - 101 \)
T^2 - T - 101
$37$
\( T^{2} - 2T - 44 \)
T^2 - 2*T - 44
$41$
\( T^{2} - 6T - 11 \)
T^2 - 6*T - 11
$43$
\( T^{2} + 7T + 1 \)
T^2 + 7*T + 1
$47$
\( T^{2} - 12T + 31 \)
T^2 - 12*T + 31
$53$
\( T^{2} - 12T + 16 \)
T^2 - 12*T + 16
$59$
\( T^{2} - 15T + 45 \)
T^2 - 15*T + 45
$61$
\( (T - 3)^{2} \)
(T - 3)^2
$67$
\( T^{2} - 16T + 19 \)
T^2 - 16*T + 19
$71$
\( T^{2} - 9T + 19 \)
T^2 - 9*T + 19
$73$
\( T^{2} - 4T - 41 \)
T^2 - 4*T - 41
$79$
\( T^{2} - 10T - 20 \)
T^2 - 10*T - 20
$83$
\( T^{2} - 3T - 29 \)
T^2 - 3*T - 29
$89$
\( T^{2} - 12T + 31 \)
T^2 - 12*T + 31
$97$
\( (T - 13)^{2} \)
(T - 13)^2
show more
show less