Some congruences modulo 2, 8 and 12 for Andrews' singular overpartitions

Recently, G. E. Andrews defined combinatorial objects which he called -singular overpartitions, overpartitions of in which no part is divisible by and only parts may be overlined. Let the number of -singular overpartitions of be\linebreak denoted by . Andrews and Chen, Hirschhorn and Sellers noted numerous congruences modulo for . The object of this paper is to obtain new congruences modulo for and modulo and for