def ith_magical_component(omega, zvee, g):
    '''Given a form omega on AS cover, element g of group AS.group and normal basis element zmag, find the decomposition
    sum_g g(zmag) omega_g and return omega_g.'''
    z_vee_g = zvee.group_action(g)
    new_form = z_vee_g*omega
    return new_form.trace()