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.'''
    AS = omega.curve
    p = AS.characteristic
    z_vee_fct = zvee.group_action(g).function
    new_form = as_form(AS, z_vee_fct*omega.form)
    return new_form.trace2()