[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
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
|
\(11\) |
\(1\) |
\(17\) |
\(-1\) |
\(43\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{69} + 11 T_{2}^{68} - 41 T_{2}^{67} - 869 T_{2}^{66} - 346 T_{2}^{65} + 31814 T_{2}^{64} + 65777 T_{2}^{63} - 711205 T_{2}^{62} - 2329125 T_{2}^{61} + 10709178 T_{2}^{60} + 48838922 T_{2}^{59} - 111493168 T_{2}^{58} + \cdots + 5248 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8041))\).