Ok, first e.preventDefault();
it's not a Jquery element, it's a method of javascript, now what it's true it's if you add this method you avoid the submit the event, now what you could do it's send the form by ajax something like this
$('#subscription_order_form').submit(function(e){
$.ajax({
url: $(this).attr('action'),
data : $(this).serialize(),
success : function (data){
}
});
e.preventDefault();
});