[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
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
|
\(5\) |
\(-1\) |
\(11\) |
\(1\) |
\(19\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{24} - 4 T_{2}^{23} - 137 T_{2}^{22} + 520 T_{2}^{21} + 8147 T_{2}^{20} - 29129 T_{2}^{19} - 275730 T_{2}^{18} + 921785 T_{2}^{17} + 5849056 T_{2}^{16} - 18149924 T_{2}^{15} - 80686705 T_{2}^{14} + \cdots + 1815552000 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1045))\).