# SageMath code for working with modular form 15210.2.a.dh


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
B = ModularForms(chi, 1).cuspidal_submodule().basis()
N = [B[i] for i in range(len(B))]

# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [3,-3,0,3,3,0,6,-3,0,-3,0,0,0,-6,0,3,7,0,-1,3,0,0,-3,0,3,0,0,
6,0,0,16,-3,0,-7,6,0,20,1,0,-3,-17,0,9,0,0,3,-7,0,5,-3,0,0,-3,0,0,-6,0,
0,-7,0,5,-16,0,3,0,0,17,7,0,-6,7,0,3,-20,0,-1,7,0,17,3,0,17,-6,0,7,-9,
0,0,3,0,0,-3,0,7,-1,0,24,-5,0,3]
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