[N,k,chi] = [825,2,Mod(181,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.181");
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
\( T_{2}^{116} - 3 T_{2}^{115} + 46 T_{2}^{114} - 116 T_{2}^{113} + 1134 T_{2}^{112} - 2627 T_{2}^{111} + 20690 T_{2}^{110} - 45716 T_{2}^{109} + 312863 T_{2}^{108} - 669700 T_{2}^{107} + 4086294 T_{2}^{106} - 8492312 T_{2}^{105} + \cdots + 262278025 \)
acting on \(S_{2}^{\mathrm{new}}(825, [\chi])\).