[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6038.1");
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
\(2\)
\(-1\)
\(3019\)
\(1\)
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6038))\).
$p$
$F_p(T)$
$2$
\( (T - 1)^{2} \)
(T - 1)^2
$3$
\( T^{2} + 3T + 1 \)
T^2 + 3*T + 1
$5$
\( T^{2} + 5T + 5 \)
T^2 + 5*T + 5
$7$
\( (T + 3)^{2} \)
(T + 3)^2
$11$
\( T^{2} + 7T + 11 \)
T^2 + 7*T + 11
$13$
\( (T + 3)^{2} \)
(T + 3)^2
$17$
\( T^{2} + 6T - 11 \)
T^2 + 6*T - 11
$19$
\( (T + 3)^{2} \)
(T + 3)^2
$23$
\( T^{2} + 6T - 11 \)
T^2 + 6*T - 11
$29$
\( T^{2} + 14T + 44 \)
T^2 + 14*T + 44
$31$
\( T^{2} + T - 31 \)
T^2 + T - 31
$37$
\( T^{2} - 3T - 9 \)
T^2 - 3*T - 9
$41$
\( T^{2} - 125 \)
T^2 - 125
$43$
\( T^{2} + 14T + 44 \)
T^2 + 14*T + 44
$47$
\( T^{2} - 3T - 99 \)
T^2 - 3*T - 99
$53$
\( (T + 9)^{2} \)
(T + 9)^2
$59$
\( T^{2} + 24T + 139 \)
T^2 + 24*T + 139
$61$
\( T^{2} + 7T + 11 \)
T^2 + 7*T + 11
$67$
\( T^{2} + 3T - 9 \)
T^2 + 3*T - 9
$71$
\( T^{2} + 6T - 71 \)
T^2 + 6*T - 71
$73$
\( T^{2} + 12T - 9 \)
T^2 + 12*T - 9
$79$
\( T^{2} - 3T - 9 \)
T^2 - 3*T - 9
$83$
\( T^{2} - 14T - 31 \)
T^2 - 14*T - 31
$89$
\( T^{2} + 9T - 131 \)
T^2 + 9*T - 131
$97$
\( T^{2} - 32T + 251 \)
T^2 - 32*T + 251
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