[N,k,chi] = [966,2,Mod(25,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 44, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.25");
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
\( T_{5}^{160} + 2 T_{5}^{159} - 25 T_{5}^{158} - 78 T_{5}^{157} + 193 T_{5}^{156} + 2045 T_{5}^{155} + 4012 T_{5}^{154} - 31174 T_{5}^{153} - 178941 T_{5}^{152} - 181654 T_{5}^{151} + 2659035 T_{5}^{150} + 12314925 T_{5}^{149} + \cdots + 10\!\cdots\!01 \)
acting on \(S_{2}^{\mathrm{new}}(966, [\chi])\).