[N,k,chi] = [666,4,Mod(1,666)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(666, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("666.1");
S:= CuspForms(chi, 4);
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 \(\beta = \sqrt{11}\).
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
\(2\)
\(-1\)
\(3\)
\(-1\)
\(37\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} - 14T_{5} - 50 \)
T5^2 - 14*T5 - 50
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(666))\).
$p$
$F_p(T)$
$2$
\( (T - 2)^{2} \)
(T - 2)^2
$3$
\( T^{2} \)
T^2
$5$
\( T^{2} - 14T - 50 \)
T^2 - 14*T - 50
$7$
\( T^{2} - 4T - 172 \)
T^2 - 4*T - 172
$11$
\( T^{2} - 44T - 616 \)
T^2 - 44*T - 616
$13$
\( T^{2} + 32T - 140 \)
T^2 + 32*T - 140
$17$
\( T^{2} - 114T + 1390 \)
T^2 - 114*T + 1390
$19$
\( T^{2} + 12T - 2120 \)
T^2 + 12*T - 2120
$23$
\( T^{2} - 166T + 5998 \)
T^2 - 166*T + 5998
$29$
\( T^{2} - 114T - 2570 \)
T^2 - 114*T - 2570
$31$
\( T^{2} - 32T - 44800 \)
T^2 - 32*T - 44800
$37$
\( (T + 37)^{2} \)
(T + 37)^2
$41$
\( T^{2} - 268T + 17780 \)
T^2 - 268*T + 17780
$43$
\( T^{2} + 480T + 6736 \)
T^2 + 480*T + 6736
$47$
\( T^{2} - 568T - 4528 \)
T^2 - 568*T - 4528
$53$
\( T^{2} - 440T + 25124 \)
T^2 - 440*T + 25124
$59$
\( T^{2} - 746T + 92654 \)
T^2 - 746*T + 92654
$61$
\( T^{2} - 220T + 3476 \)
T^2 - 220*T + 3476
$67$
\( T^{2} - 300T - 218444 \)
T^2 - 300*T - 218444
$71$
\( T^{2} - 240944 \)
T^2 - 240944
$73$
\( T^{2} - 1020 T + 106936 \)
T^2 - 1020*T + 106936
$79$
\( T^{2} - 780T + 85176 \)
T^2 - 780*T + 85176
$83$
\( T^{2} + 820T + 155384 \)
T^2 + 820*T + 155384
$89$
\( T^{2} - 90T - 175394 \)
T^2 - 90*T - 175394
$97$
\( T^{2} - 128 T - 3085804 \)
T^2 - 128*T - 3085804
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