[N,k,chi] = [712,2,Mod(25,712)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(712, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("712.25");
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
\( T_{3}^{100} - 20 T_{3}^{98} + 44 T_{3}^{97} + 277 T_{3}^{96} - 880 T_{3}^{95} - 2439 T_{3}^{94} + 10659 T_{3}^{93} + 18969 T_{3}^{92} - 94314 T_{3}^{91} - 153704 T_{3}^{90} + 762663 T_{3}^{89} + 1344841 T_{3}^{88} + \cdots + 2111209 \)
acting on \(S_{2}^{\mathrm{new}}(712, [\chi])\).