[N,k,chi] = [201,3,Mod(7,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 23]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.7");
S:= CuspForms(chi, 3);
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
\( T_{2}^{220} + 35 T_{2}^{218} + 11 T_{2}^{217} + 432 T_{2}^{216} + 837 T_{2}^{215} - 1961 T_{2}^{214} + 23914 T_{2}^{213} - 123118 T_{2}^{212} + 276880 T_{2}^{211} - 1001893 T_{2}^{210} - 1149421 T_{2}^{209} + \cdots + 30\!\cdots\!81 \)
acting on \(S_{3}^{\mathrm{new}}(201, [\chi])\).