# SageMath code for working with modular form 10005.2.a.c


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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(10005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,-1,-1,-1,1,1,-4,3,1,-1,6,1,-6,4,-1,-1,0,-1,-4,-1,4,-6,-1,-3,
1,6,-1,4,1,1,10,-5,-6,0,-4,-1,-6,4,6,3,-10,-4,12,-6,1,1,8,1,9,-1,0,6,-6,
1,6,-12,4,-1,-2,1,2,-10,-4,7,-6,6,-12,0,1,4,2,3,4,6,-1,4,-24,-6,0,-1,1,
10,12,-4,0,-12,-1,18,14,-1,24,1,-10,-8,-4,5,-6,-9,6,-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