The Noether-Lefschetz (NL) divisors on moduli space of quasi-polarized K3 surfaces are the loci where the Picard number is greater than one. Maulik and Pandharipande have conjectured that NL-divisros will span the Picard group of the moduli space. I will talk about this problem from both geometry and arithmetic. In particular, we verify this conjecture via GIT when the degree of the K3 surface is small. I will also talk about the general case and the relation to automorphic representation theory. A conjectural approach to this problem may be discussed at the end of this talk. This is joint work with Zhiyu Tian.