# SageMath code for working with modular form 42483.2.a.c


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42483, 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(42483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,-1,-1,0,1,0,3,1,0,-4,1,-2,0,0,-1,0,-1,-4,0,0,4,4,-3,-5,
2,-1,0,0,0,4,-5,4,0,0,-1,8,4,2,0,-8,0,4,4,0,-4,8,1,0,5,0,2,-6,1,0,0,4,
0,-12,0,-8,-4,0,7,0,-4,12,0,-4,0,12,3,0,-8,5,4,0,-2,4,0,1,8,12,0,0,-4,
0,-12,10,0,0,-4,-4,-8,0,5,-16,0,-4,5]
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