[N,k,chi] = [770,2,Mod(61,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([0, 25, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.61");
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
\( T_{3}^{128} + 35 T_{3}^{126} + 506 T_{3}^{124} - 72 T_{3}^{123} + 2243 T_{3}^{122} - 1440 T_{3}^{121} - 36362 T_{3}^{120} + 4548 T_{3}^{119} - 800392 T_{3}^{118} + 582418 T_{3}^{117} - 7613782 T_{3}^{116} + \cdots + 38\!\cdots\!16 \)
acting on \(S_{2}^{\mathrm{new}}(770, [\chi])\).