Since Ms. Cole's sixth-level math class has 40 students and four times as many students in her fourth-level class, there are 4*40 = <<4*40=160>>160 in her fourth-level math class.
For the two levels, Ms. Cole teaches math to 160+40 = <<160+40=200>>200 students.
If the number of students in her seventh-level math class is twice that in the fourth-level math class, then she teaches 2*160 = <<2*160=320>>320 students in the seventh-level math class.
Ms. Cole teaches 320+200 = <<320+200=520>>520 math students in the school.
#### 520