[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1875.1");
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
|
\(3\) |
\(-1\) |
\(5\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{24} - T_{2}^{23} - 162 T_{2}^{22} + 148 T_{2}^{21} + 11359 T_{2}^{20} - 9556 T_{2}^{19} - 452004 T_{2}^{18} + 354292 T_{2}^{17} + 11247807 T_{2}^{16} - 8329949 T_{2}^{15} - 181797882 T_{2}^{14} + \cdots + 2143086336 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1875))\).