[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6039.1");
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
|
\(3\) |
\(1\) |
\(11\) |
\(1\) |
\(61\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{25} - 5 T_{2}^{24} - 25 T_{2}^{23} + 155 T_{2}^{22} + 226 T_{2}^{21} - 2056 T_{2}^{20} - 615 T_{2}^{19} + 15295 T_{2}^{18} - 4003 T_{2}^{17} - 70329 T_{2}^{16} + 40855 T_{2}^{15} + 207955 T_{2}^{14} - 161462 T_{2}^{13} + \cdots - 657 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6039))\).