sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("153.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
This newform subspace can be constructed as the kernel of the linear operator
T240+2688T236−192T235+5184T233+2794362T232+⋯+4964982194176
acting on S4new(153,[χ]).