# SageMath code for working with modular form 11025.2.a.da


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11025, 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(11025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [3,-2,0,6,0,0,0,-6,0,0,10,0,7,0,0,4,-2,0,1,0,0,-2,-10,0,0,0,0,
0,4,0,1,-24,0,12,0,0,-11,-28,0,0,-2,0,3,30,0,-16,-2,0,0,0,0,24,-4,0,0,
0,0,14,-4,0,22,30,0,20,0,0,15,-10,0,0,16,0,9,6,0,30,0,0,-7,0,0,-6,14,0,
0,18,0,-40,30,0,0,18,0,32,0,0,-4,0,0,0]
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