[N,k,chi] = [750,2,Mod(19,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(50))
chi = DirichletCharacter(H, H._module([0, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.19");
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
\( T_{7}^{240} - 235 T_{7}^{238} - 50 T_{7}^{237} + 29150 T_{7}^{236} + 11750 T_{7}^{235} - 2537660 T_{7}^{234} - 1450850 T_{7}^{233} + 174300620 T_{7}^{232} + 125000200 T_{7}^{231} - 10050921831 T_{7}^{230} + \cdots + 11\!\cdots\!76 \)
acting on \(S_{2}^{\mathrm{new}}(750, [\chi])\).