# SageMath code for working with modular form 18590.2.a.h


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18590, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [1,-1,2,1,-1,-2,-4,-1,1,1,1,2,0,4,-2,1,-2,-1,0,-1,-8,-1,-4,-2,
1,0,-4,-4,-8,2,0,-1,2,2,4,1,-6,0,0,1,8,8,4,1,-1,4,6,2,9,-1,-4,0,-4,4,-1,
4,0,8,-4,-2,8,0,-4,1,0,-2,12,-2,-8,-4,-16,-1,2,6,2,0,-4,0,-12,-1,-11,-8,
4,-8,2,-4,-16,-1,-6,1,0,-4,0,-6,0,-2,-12,-9,1,1]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)

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