[N,k,chi] = [495,2,Mod(23,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 9, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.23");
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
\( T_{2}^{116} + 2 T_{2}^{115} - T_{2}^{114} - 8 T_{2}^{113} - 229 T_{2}^{112} - 412 T_{2}^{111} + 290 T_{2}^{110} + 1618 T_{2}^{109} + 29728 T_{2}^{108} + 50246 T_{2}^{107} - 43046 T_{2}^{106} - 200096 T_{2}^{105} - 2589232 T_{2}^{104} + \cdots + 44302336 \)
acting on \(S_{2}^{\mathrm{new}}(495, [\chi])\).