Get sum of every category for last 6 months laravel 5

I have a query:

            $paymentList = DB::table('tbl_student_payment_sub_head_details')
                ->if($Class, 'class_name', "=", $Class)
                ->if($Group, 'group_name', "=", $Group)
                ->if($BranchShiftVersion, 'institute_branch_version_id', "=", $BranchShiftVersion)
                ->if($Year, 'acc_year', "=", $Year)
                ->orderBy('id')
                ->lists('name', 'id');

which returns following array.

Array
(
    [1] => Tuition Fee
    [2] => Session Fees
    [3] => Diary, Syllabus, Calendar, ID Card   
    [4] => ICT Fee  
    [5] => Exam Fee Half Yearly
    [6] => Exam Fee Annual  
    [7] => Mid Term Fee 
    [11] => Delay Fine  
    [12] => Absence fine    
    [13] => TC Fee  
    [14] => Other Fee   
    [15] => Admission Fee
    [16] => Arear Due
    [17] => Delay Fine 2
    [18] => Delay Fine 3
    [19] => Delay Fine 4
)

I have another table named tbl_received_student_payment_sub_heads which stores student payment information of some category from above. Columns that this table have:

'id' (pk), 'student_payment_id' (fk), 'payment_amount', 'student_id' (fk), 'create_time'.

Now i am looking for a query, which will return the total payment of every category of each students for last 6 months/given range. It also should return 0 if a student did not pay anything for a category. Can anything help me out with that?

(Note: My application is developed in laravel 5.1)

via Chebli Mohamed