  We give a new simple formula for the energy function of a level $1$ perfect
crystal of type $C_n^{(1)}$ introduced by Kang, Kashiwara and Misra. We use
this to give several expressions for the characters of level $1$ standard
modules as generating functions for different types of partitions. We then
relate one of these formulas to the difference conditions in the conjectural
partition identity of Capparelli, Meurman, Primc and Primc, and prove that
their conjecture is true for all level $1$ standard modules. Finally, we
propose a non-specialised generalisation of their conjecture.
