[N,k,chi] = [671,2,Mod(70,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("671.70");
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
\( T_{2}^{236} - 2 T_{2}^{235} + 92 T_{2}^{234} - 188 T_{2}^{233} + 4455 T_{2}^{232} - 9182 T_{2}^{231} + 150963 T_{2}^{230} - 311394 T_{2}^{229} + 4018926 T_{2}^{228} - 8259045 T_{2}^{227} + 89420855 T_{2}^{226} + \cdots + 102191881 \)
acting on \(S_{2}^{\mathrm{new}}(671, [\chi])\).