[N,k,chi] = [667,2,Mod(59,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([14, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("667.59");
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
\( T_{2}^{280} + 44 T_{2}^{278} + 1082 T_{2}^{276} - 8 T_{2}^{275} + 19446 T_{2}^{274} - 540 T_{2}^{273} + 285429 T_{2}^{272} - 17853 T_{2}^{271} + 3635658 T_{2}^{270} - 401210 T_{2}^{269} + 41747513 T_{2}^{268} + \cdots + 39\!\cdots\!21 \)
acting on \(S_{2}^{\mathrm{new}}(667, [\chi])\).