[N,k,chi] = [1003,4,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1003.1");
S:= CuspForms(chi, 4);
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.
\( p \) |
Sign
|
\(17\) |
\(1\) |
\(59\) |
\(1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{59} - 13 T_{2}^{58} - 269 T_{2}^{57} + 4097 T_{2}^{56} + 31923 T_{2}^{55} - 605911 T_{2}^{54} - 2105624 T_{2}^{53} + 55909895 T_{2}^{52} + 72729444 T_{2}^{51} - 3610196232 T_{2}^{50} + \cdots + 55\!\cdots\!88 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1003))\).