[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
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
\(7\)
\(1\)
\(863\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} + 1 \)
T2 + 1
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6041))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{2} \)
(T + 1)^2
$3$
\( T^{2} - 3T + 1 \)
T^2 - 3*T + 1
$5$
\( T^{2} - T - 1 \)
T^2 - T - 1
$7$
\( (T + 1)^{2} \)
(T + 1)^2
$11$
\( T^{2} + 3T + 1 \)
T^2 + 3*T + 1
$13$
\( T^{2} - 9T + 19 \)
T^2 - 9*T + 19
$17$
\( T^{2} + 2T - 4 \)
T^2 + 2*T - 4
$19$
\( T^{2} - 3T - 29 \)
T^2 - 3*T - 29
$23$
\( T^{2} + T - 31 \)
T^2 + T - 31
$29$
\( T^{2} - 20 \)
T^2 - 20
$31$
\( T^{2} + 4T - 16 \)
T^2 + 4*T - 16
$37$
\( T^{2} + 11T + 19 \)
T^2 + 11*T + 19
$41$
\( T^{2} - 80 \)
T^2 - 80
$43$
\( T^{2} - 2T - 44 \)
T^2 - 2*T - 44
$47$
\( T^{2} + 2T - 4 \)
T^2 + 2*T - 4
$53$
\( T^{2} - 7T - 49 \)
T^2 - 7*T - 49
$59$
\( T^{2} + 19T + 89 \)
T^2 + 19*T + 89
$61$
\( T^{2} - 14T + 4 \)
T^2 - 14*T + 4
$67$
\( T^{2} + 21T + 99 \)
T^2 + 21*T + 99
$71$
\( T^{2} - 4T - 16 \)
T^2 - 4*T - 16
$73$
\( T^{2} - 3T - 9 \)
T^2 - 3*T - 9
$79$
\( T^{2} + 25T + 155 \)
T^2 + 25*T + 155
$83$
\( T^{2} - 22T + 116 \)
T^2 - 22*T + 116
$89$
\( T^{2} - 4T - 76 \)
T^2 - 4*T - 76
$97$
\( T^{2} + 3T - 9 \)
T^2 + 3*T - 9
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