[N,k,chi] = [784,2,Mod(65,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 0, 20]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.65");
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
\( T_{3}^{60} + T_{3}^{59} - 2 T_{3}^{58} + 4 T_{3}^{57} - 35 T_{3}^{56} - 207 T_{3}^{55} + 124 T_{3}^{54} - 538 T_{3}^{53} + 1273 T_{3}^{52} + 728 T_{3}^{51} - 17455 T_{3}^{50} - 149413 T_{3}^{49} + 371884 T_{3}^{48} + 1504928 T_{3}^{47} + \cdots + 6889 \)
acting on \(S_{2}^{\mathrm{new}}(784, [\chi])\).