# SageMath code for working with modular form 15730.2.a.bt


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [3,-3,1,3,-3,-1,2,-3,8,3,0,1,3,-2,-1,3,-3,-8,5,-3,-13,0,0,-1,
3,-3,-14,2,4,1,-17,-3,0,3,-2,8,0,-5,1,3,13,13,10,0,-8,0,-17,1,1,-3,-4,
3,-1,14,0,-2,29,-4,-6,-1,11,17,26,3,-3,0,9,-3,-9,2,-1,-8,9,0,1,5,0,-1,
-5,-3,-9,-13,-1,-13,3,-10,-23,0,-13,8,2,0,17,17,-5,-1,2,-1,0,3]
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