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I would advise to create a nested list of objects:

a = [[M.diff_form(1, name='a_{}{}'.format(i, j), 
                  latex_name='a_{{{}{}}}'.format(i, j)) 
      for j in range(4)] for i in range(4)]

Then you access to a_ij via a[i][j]. For instance (first line is input, second line is output):

a[1][3]
1-form a_13 on the 2-dimensional differentiable manifold M

and

latex(a[1][3])
a_{13}

It is possible to dynamically inject names like a_13 in the global namespace, by adding new entries in the dictionary globals(), but this is generally not recommended.