[N,k,chi] = [828,2,Mod(19,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 0, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("828.19");
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
\( T_{5}^{120} - 36 T_{5}^{118} + 924 T_{5}^{116} + 44 T_{5}^{115} - 20280 T_{5}^{114} - 5368 T_{5}^{113} + 405027 T_{5}^{112} + 111276 T_{5}^{111} - 7122858 T_{5}^{110} - 2026992 T_{5}^{109} + 111162417 T_{5}^{108} + \cdots + 37\!\cdots\!29 \)
acting on \(S_{2}^{\mathrm{new}}(828, [\chi])\).