[N,k,chi] = [690,2,Mod(7,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([0, 11, 38]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.7");
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
\( T_{7}^{240} + 88 T_{7}^{237} - 352 T_{7}^{236} + 924 T_{7}^{235} + 3872 T_{7}^{234} - 163460 T_{7}^{233} + 542862 T_{7}^{232} + 125576 T_{7}^{231} - 12594648 T_{7}^{230} + 90828496 T_{7}^{229} + \cdots + 19\!\cdots\!16 \)
acting on \(S_{2}^{\mathrm{new}}(690, [\chi])\).