New congruences for Andrews' singular overpartitions

Recently, Andrews defined the combinatorial objects which he called singular overpartitions and proved that these singular overpartitions, which depend on two parameters kappa and i, can be enumerated by the function C-kappa, i(n) which gives the number of overpartitions of n in which no part is divisible by k and only parts equivalent to +/- i (mod k) may be overlined. He also proved that C-3,(1) (9n + 3) equivalent to C-3,C-1(9n + 6) equivalent to 0 (mod 3). Chen, Hirschhorn and Sellers then found infinite families of congruences modulo 3 and modulo powers of 2 for C-3,C-1(n), C-6,C-1(n) and C-6,C-2(n). In this paper, we find new congruences for C3,1(n) modulo 4, 18 and 36, infinite families of congruences modulo 2 and 4 for C-8,C-2(n), congruences modulo 2 and 3 for C-12,C-2(n), C-12,C-4(n), and congruences modulo 2 for C-24,C-8(n) and C-48,C-16(n). We use simple p-dissections of Ramanujan's theta functions.