# SageMath code for working with modular form 29400.2.a.h


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [1,0,-1,0,0,0,0,0,1,0,-5,0,2,0,0,0,-6,0,2,0,0,0,5,0,0,0,-1,0,
-5,0,4,0,5,0,0,0,1,0,-2,0,12,0,5,0,0,0,-2,0,0,0,6,0,14,0,0,0,-2,0,-2,0,
0,0,0,0,0,0,-5,0,-5,0,-9,0,-10,0,0,0,0,0,11,0,1,0,-16,0,0,0,5,0,14,0,0,
0,-4,0,0,0,-8,0,-5,0]
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