# SageMath code for working with modular form 37479.2.a.g


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37479, 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(37479, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,1,-1,2,1,-4,-3,1,2,-4,-1,-1,-4,2,-1,-2,1,0,-2,-4,-4,0,-3,
-1,-1,1,4,10,2,0,5,-4,-2,-8,-1,2,0,-1,-6,6,-4,12,4,2,0,0,-1,9,-1,-2,1,
-6,1,-8,12,0,10,12,-2,2,0,-4,7,-2,-4,-8,2,0,-8,0,-3,-2,2,-1,0,16,-1,-8,
-2,1,6,-4,4,-4,12,10,12,2,2,4,0,0,0,0,5,10,9,-4,1]
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