[N,k,chi] = [867,2,Mod(52,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(34))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("867.52");
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
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
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.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{416} - T_{2}^{415} + 41 T_{2}^{414} - 45 T_{2}^{413} + 913 T_{2}^{412} - 1093 T_{2}^{411} + 14884 T_{2}^{410} - 19054 T_{2}^{409} + 200281 T_{2}^{408} - 269259 T_{2}^{407} + 2367488 T_{2}^{406} - 3306896 T_{2}^{405} + \cdots + 40\!\cdots\!16 \)
acting on \(S_{2}^{\mathrm{new}}(867, [\chi])\).