[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
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
|
\(37\) |
\(-1\) |
\(109\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{77} + 9 T_{2}^{76} - 73 T_{2}^{75} - 880 T_{2}^{74} + 2021 T_{2}^{73} + 40805 T_{2}^{72} - 10998 T_{2}^{71} - 1192879 T_{2}^{70} - 994027 T_{2}^{69} + 24646044 T_{2}^{68} + 39264137 T_{2}^{67} + \cdots + 5180112 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4033))\).