# SageMath code for working with modular form 7569.2.a.bm


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [9,5,0,11,4,0,5,24,0,0,-1,0,1,9,0,35,2,0,-9]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

# q-expansion: 
f.q_expansion() # note that sage often uses an isomorphic number field