# SageMath code for working with modular form 7350.2.a.bg


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [1,-1,1,1,0,-1,0,-1,1,0,2,1,-6,0,0,1,-2]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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