[N,k,chi] = [639,2,Mod(10,639)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(639, base_ring=CyclotomicField(70))
chi = DirichletCharacter(H, H._module([0, 34]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("639.10");
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
\( T_{2}^{144} - 3 T_{2}^{143} + 2 T_{2}^{142} + 3 T_{2}^{141} - 9 T_{2}^{140} - 58 T_{2}^{139} - 86 T_{2}^{138} + 660 T_{2}^{137} - 827 T_{2}^{136} + 4695 T_{2}^{135} + 4082 T_{2}^{134} - 25220 T_{2}^{133} + 45962 T_{2}^{132} - 139132 T_{2}^{131} + \cdots + 49014001 \)
acting on \(S_{2}^{\mathrm{new}}(639, [\chi])\).