Why is the ManyToManyField field not being written when processing the form?

Question

Django

I display the form, fields: Date (data), people selection field (people) and Status (status), accepting a post request, add a value to the school_class field equal to pk and save. Date, status and school_class are saved, but people are not, what's wrong?
models.py:

class SchoolClass(models.Model):
    school_class = models.CharField(max_length=10, help_text = 'Класс')
    def __str__(self):
        return self.school_class
        # Возвращает id 0_о
    def get_absolute_url(self):
        return reverse('class-detail', args=[str(self.id)])
    class Meta:
    	ordering = ['school_class']

class People(models.Model):
    first_name = models.CharField(max_length=100, help_text = 'Имя учащегося')
    last_name = models.CharField(max_length=100, help_text = 'Фамилия учащегося')
    school_class = models.ForeignKey(SchoolClass, help_text = 'Класс ученика', on_delete = models.SET_NULL, null=True)
    def __str__(self):
        return '{} {}'.format(self.first_name, self.last_name)

class State(models.Model):
    date = models.DateField(help_text = 'Дата')
    status = models.CharField(max_length=10, choices = (
        ('+', '+'),
        ('-', '-')
        ))
    people = models.ManyToManyField(People, 
        help_text = 'Фамилия и имя учащегося',
        related_name="peoples",
        blank = 'true')
    school_class = models.CharField(max_length=10)

    def __str__(self):
        return '{} {}'.format(self.date, self.people.__str__())

    def get_absolute_url(self):
        return reverse('date-detail', args=[str(self.id)])

    class Meta:
        ordering = ['date']

forms.py:

class StateForm(forms.ModelForm):
    class Meta:
        model = State
        fields = ('date', 'people', 'status')

views.py:

@login_required
def newwrite(request, pk):
    if request.method == 'POST':
        form = StateForm(request.POST)
        if form.is_valid():
            state = form.save(commit=False)
            state.school_class = pk
            state.save()
            return redirect('writeindex')
    else:
        form = StateForm()
    return render(
        request,
        'app/newwrite.html',
        context = {'form':form})