[N,k,chi] = [6041,2,Mod(1,6041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6041, 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("6041.1");
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
|
\(7\) |
\(-1\) |
\(863\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{83} + 8 T_{2}^{82} - 75 T_{2}^{81} - 754 T_{2}^{80} + 2369 T_{2}^{79} + 33869 T_{2}^{78} - 34220 T_{2}^{77} - 964839 T_{2}^{76} - 103069 T_{2}^{75} + 19565838 T_{2}^{74} + 16244910 T_{2}^{73} - 300488895 T_{2}^{72} + \cdots - 299 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6041))\).