Today I came across the following theorem of Mersmann: *There are precisely* 14 *primitive eta-products which are holomorphic modular forms of weight* $\frac{1}{2}$, [*namely*...][1]

He also proves a conjecture of Zagier to the effect that there are essentially only finitely many such products of any given weight.

I learnt these facts from Zagier's contribution to the [*The 1-2-3 of modular forms*][2] (which happens to have been metioned by Wadim Zudilin).

**Addendum** (2011/02/10)  Came across an advertisement for the book [*Eta products and thera series identities*][3] by Günter Köhler.





  [1]: http://books.google.com/books?id=tsTfnHLmgmQC&lpg=PA23&dq=subject%253A%2522Mathematics%2522%2520ramanujan%2520tau%2520function&pg=PA30#v=onepage&q=Mersmann&f=false
  [2]: http://books.google.com/books?id=tsTfnHLmgmQC&lpg=PA23&dq=subject%253A%2522Mathematics%2522%2520ramanujan%2520tau%2520function&pg=PP1#v=onepage&q&f=false
  [3]: http://www.springer.com/mathematics/numbers/book/978-3-642-16151-3