[N,k,chi] = [50,8,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 8);
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 \(\beta = 10\sqrt{31}\).
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
\(2\)
\(-1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 56T_{3} - 2316 \)
T3^2 - 56*T3 - 2316
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(50))\).
$p$
$F_p(T)$
$2$
\( (T - 8)^{2} \)
(T - 8)^2
$3$
\( T^{2} - 56T - 2316 \)
T^2 - 56*T - 2316
$5$
\( T^{2} \)
T^2
$7$
\( T^{2} - 408T - 110284 \)
T^2 - 408*T - 110284
$11$
\( T^{2} - 8904 T + 19026704 \)
T^2 - 8904*T + 19026704
$13$
\( T^{2} + 3504 T - 15790896 \)
T^2 + 3504*T - 15790896
$17$
\( T^{2} - 43648 T + 388792576 \)
T^2 - 43648*T + 388792576
$19$
\( T^{2} + 31800 T - 954255600 \)
T^2 + 31800*T - 954255600
$23$
\( T^{2} - 71656 T - 950837516 \)
T^2 - 71656*T - 950837516
$29$
\( T^{2} + 84780 T - 19030326300 \)
T^2 + 84780*T - 19030326300
$31$
\( T^{2} + 197056 T + 4879504384 \)
T^2 + 197056*T + 4879504384
$37$
\( T^{2} - 195408 T - 51511044784 \)
T^2 - 195408*T - 51511044784
$41$
\( T^{2} - 116244 T - 183681487516 \)
T^2 - 116244*T - 183681487516
$43$
\( T^{2} - 275736 T + 17685717524 \)
T^2 - 275736*T + 17685717524
$47$
\( T^{2} + 971272 T - 599256039404 \)
T^2 + 971272*T - 599256039404
$53$
\( T^{2} + 2007504 T + 504522481104 \)
T^2 + 2007504*T + 504522481104
$59$
\( T^{2} + 1046760 T - 159475001200 \)
T^2 + 1046760*T - 159475001200
$61$
\( T^{2} + 2625716 T + 1716951910564 \)
T^2 + 2625716*T + 1716951910564
$67$
\( T^{2} - 1678728 T - 2422233726604 \)
T^2 - 1678728*T - 2422233726604
$71$
\( T^{2} + 3916176 T - 4934358737856 \)
T^2 + 3916176*T - 4934358737856
$73$
\( T^{2} - 2606496 T + 296239095104 \)
T^2 - 2606496*T + 296239095104
$79$
\( T^{2} + 3863520 T - 3963839328000 \)
T^2 + 3863520*T - 3963839328000
$83$
\( T^{2} - 5183416 T - 36935334540236 \)
T^2 - 5183416*T - 36935334540236
$89$
\( T^{2} - 16735020 T + 66278240560100 \)
T^2 - 16735020*T + 66278240560100
$97$
\( T^{2} - 12604608 T - 1192948931584 \)
T^2 - 12604608*T - 1192948931584
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