[N,k,chi] = [354,2,Mod(11,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(58))
chi = DirichletCharacter(H, H._module([29, 25]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.11");
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
\( T_{5}^{280} - 23 T_{5}^{278} - 145 T_{5}^{277} + 542 T_{5}^{276} + 2581 T_{5}^{275} + 812 T_{5}^{274} - 59044 T_{5}^{273} + 29236 T_{5}^{272} + 363515 T_{5}^{271} + 1045619 T_{5}^{270} - 10160179 T_{5}^{269} + \cdots + 17\!\cdots\!96 \)
acting on \(S_{2}^{\mathrm{new}}(354, [\chi])\).