# SageMath code for working with modular form 30345.2.a.r


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30345, 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(30345, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,0,1,-2,1,0,-1,0,1,0,-2,-2,-5,0,1,4,0,0,2,-2,-1,0,1,0,1,0,1,
2,-8,0,-1,0,-2,0,-1,-2,3,0,-5,0,7,0,0,4,1,0,-1,4,1,0,0,10,-8,0,-2,0,2,
0,0,-2,7,0,-1,-8,-5,0,16,0,1,0,10,0,8,0,1,-4,2,0,6,4,1,0,-13,2,0,0,-8,
0,-2,0,5,-2,-1,0,2,0,6,0,-2,-2]
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