[N,k,chi] = [473,2,Mod(23,473)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(473, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("473.23");
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
\( T_{2}^{216} - 2 T_{2}^{215} + 50 T_{2}^{214} - 102 T_{2}^{213} + 1399 T_{2}^{212} - 2892 T_{2}^{211} + 28839 T_{2}^{210} - 59524 T_{2}^{209} + 486847 T_{2}^{208} - 992249 T_{2}^{207} + 7115853 T_{2}^{206} + \cdots + 23\!\cdots\!61 \)
acting on \(S_{2}^{\mathrm{new}}(473, [\chi])\).