How to make a table with multirows and multi cell and color?

Question

I want to make a table like the figure attached.

Here is my code:

\documentclass{article}
\usepackage[table, svgnames, dvipsnames]{xcolor}
\usepackage{makecell, cellspace, caption}
\usepackage[table]{xcolor}
\usepackage{multirow} 
\usepackage{booktabs}
\usepackage[tableposition=above]{caption}
\usepackage{pifont}
\usepackage{multirow} %for multirow
\setlength\cellspacetoplimit{2pt}
\setlength\cellspacebottomlimit{5pt}
\begin{document}
\begin{table}
        \centering\captionsetup{justification = centering}
        \caption{Different quantum number combinations}
        %{\centering}
        \label{tabla-numeros}
        \begin{tabular}{|Sc|Sc|Sc|Sc|Sc|}
            \hline
            \rowcolor{Gainsboro!60}
            \makecell{\textbf{Level}\ $n$} & \makecell{\textbf{Sub-level}\ $l = 0, 1, ...., n - 1$} & \makecell{\textbf{Orbital} ($2l+1$)\ $m_l = -l,...,0,...,+l $}  & \makecell{\textbf{Spín} \ $m_s$}   &     \makecell{\textbf{No. of electrons} \ $2n^2$}\
            \hline
            \rowcolor{blue!20}
            \multirow{2}{}{1} &   \multirow{2}{}{0} &   \multirow{2}{}{0 (s)} & $+\frac{1}{2}$  &  \multirow{2}{}{2} \
            \rowcolor{blue!20}
                                            &                                   &                                           & $-\frac{1}{2}$        &                               \

             \rowcolor{green!20} 
              \makecell{\multirow{3}{}{2}} &    \makecell{\multirow{2}{}{0}} & \makecell{\multirow{2}{}{0 (s)}} & $+\frac{1}{2}$   &      \makecell{\multirow{8}{}{8}}       \
             \rowcolor{green!20}
                                            &                                   &                                           & $-\frac{1}{2}$        &                               \
             \rowcolor{green!20}
                &   \multirow{2}{}{} & \multirow{2}{}{-1 ($p_x$)} & $+\frac{1}{2}$   &    \multirow{8}{}{8}       \
             \rowcolor{green!20}
                                            &                                   &                                           & $-\frac{1}{2}$        &                               \
             \rowcolor{green!20}
                &   \multirow{2}{}{1} & \multirow{2}{}{0 ($p_y$)} & $+\frac{1}{2}$   &    \multirow{8}{}{8}       \
             \rowcolor{green!20}
                                            &                                   &                                           & $-\frac{1}{2}$        &                               \
             \rowcolor{green!20}
                &   \multirow{2}{}{} & \multirow{2}{}{+1 ($p_z$)} & $+\frac{1}{2}$   &    \multirow{8}{*}{8}       \
             \rowcolor{green!20}
                                            &                                   &                                           & $-\frac{1}{2}$        &                               \

             \rowcolor{yellow!20}
              &  &  &   & \
             \rowcolor{pink!20}
              &  &  &   &\
            \hline
        \end{tabular}
\end{table}
\end{document}

I have problems with the multirow command, because in the first column I can't write the number 2 in the midle parte of the cells coulored with green. I have the same problem with the cells in yellow and pink.
I will appreciate your help.