[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6033.1");
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.
\( p \) |
Sign
|
\(3\) |
\(-1\) |
\(2011\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{71} + 11 T_{2}^{70} - 37 T_{2}^{69} - 825 T_{2}^{68} - 480 T_{2}^{67} + 28663 T_{2}^{66} + 63332 T_{2}^{65} - 607422 T_{2}^{64} - 2080335 T_{2}^{63} + 8646624 T_{2}^{62} + 41256389 T_{2}^{61} - 84474552 T_{2}^{60} + \cdots + 476 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6033))\).