[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, 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("4030.1");
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
\(2\)
\(1\)
\(5\)
\(1\)
\(13\)
\(-1\)
\(31\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 2T_{3} - 4 \)
T3^2 - 2*T3 - 4
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4030))\).
$p$
$F_p(T)$
$2$
\( (T + 1)^{2} \)
(T + 1)^2
$3$
\( T^{2} - 2T - 4 \)
T^2 - 2*T - 4
$5$
\( (T + 1)^{2} \)
(T + 1)^2
$7$
\( T^{2} + T - 11 \)
T^2 + T - 11
$11$
\( T^{2} + 6T + 4 \)
T^2 + 6*T + 4
$13$
\( (T - 1)^{2} \)
(T - 1)^2
$17$
\( T^{2} - 7T + 11 \)
T^2 - 7*T + 11
$19$
\( T^{2} + 3T - 29 \)
T^2 + 3*T - 29
$23$
\( T^{2} + 5T - 5 \)
T^2 + 5*T - 5
$29$
\( T^{2} - 17T + 71 \)
T^2 - 17*T + 71
$31$
\( (T + 1)^{2} \)
(T + 1)^2
$37$
\( T^{2} + 9T - 11 \)
T^2 + 9*T - 11
$41$
\( T^{2} - 10T - 20 \)
T^2 - 10*T - 20
$43$
\( T^{2} - 6T + 4 \)
T^2 - 6*T + 4
$47$
\( T^{2} + 11T - 1 \)
T^2 + 11*T - 1
$53$
\( (T - 10)^{2} \)
(T - 10)^2
$59$
\( T^{2} - 7T + 1 \)
T^2 - 7*T + 1
$61$
\( T^{2} + 7T - 89 \)
T^2 + 7*T - 89
$67$
\( T^{2} - 8T - 4 \)
T^2 - 8*T - 4
$71$
\( T^{2} - 4T - 76 \)
T^2 - 4*T - 76
$73$
\( T^{2} + 2T - 4 \)
T^2 + 2*T - 4
$79$
\( T^{2} - 24T + 124 \)
T^2 - 24*T + 124
$83$
\( T^{2} - 3T - 9 \)
T^2 - 3*T - 9
$89$
\( T^{2} - 15T + 45 \)
T^2 - 15*T + 45
$97$
\( T^{2} + 21T + 109 \)
T^2 + 21*T + 109
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