Inspired by Mohammad Rasel Parvej

Let $P(x) \in \mathbb{R}[x]$ be a Polynomial in x defined as follows: $P(x) = x^{2016} + x^{2013} + x^{2010} + x^{2007} + ... + x^6 + x^3 +1$ ; $(P: \mathbb{R} \to \mathbb{R})$

Let $R(x)=C$ be the Polynomial that is obtained as remainder when $P(x)$ is divided by $x^3 -3$

$C$ is a Constant Natural Number. Find the number of $1$ 's in Base-3(ternary base) in the representation of $C$ .

Inspiration

Bonus : How many 1's would have $C$ if $P : \mathbb{Z}_3 \rightarrow \mathbb{Z}_3$ ?