[N,k,chi] = [950,2,Mod(61,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(90))
chi = DirichletCharacter(H, H._module([72, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.61");
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
\( T_{3}^{600} + 15 T_{3}^{596} + 42 T_{3}^{595} - 2705 T_{3}^{594} + 2271 T_{3}^{593} - 5376 T_{3}^{592} + 13890 T_{3}^{591} + 12024 T_{3}^{590} - 333228 T_{3}^{589} + 2090375 T_{3}^{588} - 7105839 T_{3}^{587} + \cdots + 14\!\cdots\!01 \)
acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).