DRF nested serializers - Filtering data on child serializers

I am trying to use nested serializer. How do I use the root serializer to filter data on the grandchild serializer?

School and Program have a many to many relationship So that any school can subscribe to any program. Each school has classes and those classes are part of a program, that's why PClass has foreign keys to both School and program.

When I call my api .../api/school/1 I want to get all the programs that school subscribes to and which classes are available in each program (in that school)

class School(TimeStampedModel, SoftDeletableModel):
    name = models.CharField(max_length=40)
    slug = models.SlugField(max_length=40, default='', blank=True)

class Program(TimeStampedModel, SoftDeletableModel):
    name = models.CharField(max_length=50, unique=True)
    slug = models.SlugField(max_length=50,default='',blank=True, unique=True)
    description = models.CharField(max_length=100, blank=True)
    school = models.ForeignKey(School, blank=True, null=True, related_name="programs")

class PClass(TimeStampedModel, SoftDeletableModel):
    name = models.CharField(max_length=50)
    slug = models.SlugField(max_length=50,default='',blank=True)
    description = models.CharField(max_length=100)
    program = models.ForeignKey(Program, related_name="classes")
    school = models.ForeignKey(School, related_name="classes")

and the following serializers:

class SchoolSerializer( serializers.ModelSerializer):
    programs = ProgramSerializer(source='get_programas',many=True,read_only=True)
    class Meta:
        model = School
        fields = '__all__'
        lookup_field = 'slug'
        extra_kwargs = {
            'url': {'lookup_field': 'slug'}
        }

class PClassSerializer(serializers.ModelSerializer):
    class Meta:
        model = Class
        fields = ('name','slug')

class ProgramSerializer(serializers.ModelSerializer):
    school = serializers.SlugRelatedField(queryset=School.objects.all(),
                                            slug_field='name',
                                            required=False)
    classes = PClassSerializer(many=True,read_only=True)
    class Meta:
        model = Program
        exclude = ('id',)
        lookup_field = 'slug'
        extra_kwargs = {
            'url': {'lookup_field': 'slug'}
        }

is this possible? or is it a problem with the way I set up my models?