How do I select a subset of a DataFrame based on one level of a MultiIndex

Let

df = pd.DataFrame({"v":range(12)}, index=pd.MultiIndex.from_product([["a","b","c"],[1,2,3,4]]))

and suppose I want to select only rows with the first level being a or c:

      v
a 1   0
  2   1
  3   2
  4   3
c 1   8
  2   9
  3  10
  4  11

I can do:

df[df.index.to_frame()[0].isin(("a","c"))]

but this creates an intermediate frame which seems like a waste.

Is there a better way?