[N,k,chi] = [725,2,Mod(146,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([6, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("725.146");
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
\( T_{2}^{128} + 45 T_{2}^{126} - 3 T_{2}^{125} + 1116 T_{2}^{124} - 127 T_{2}^{123} + 20215 T_{2}^{122} - 2948 T_{2}^{121} + 299503 T_{2}^{120} - 50370 T_{2}^{119} + 3812817 T_{2}^{118} - 715856 T_{2}^{117} + 42829347 T_{2}^{116} + \cdots + 1679616 \)
acting on \(S_{2}^{\mathrm{new}}(725, [\chi])\).