Recently, Chen and Kiming studied the theta operator on modular forms modulo prime powers
p
m
{p^{m}}
, where
p
≥
5
{p\geq 5}
and
m
≥
2
{m\geq 2}
. In this paper, we study mod
p
m
{p^{m}}
filtrations and mod
p
m
{p^{m}}
theta cycles. We give a bound on some elements in the mod
p
m
{p^{m}}
theta cycle (
m
≥
2
{m\geq 2}
), and we exactly compute those values in the case that
m
=
2
{m=2}
.
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