I need to draw a diamond with a plus sign in the center and then be able to add limits to it, as shown in the figure.

I need to create one diamond big and bold and another one small and not bold, such that it would follow the same structure of \bigotimes and \otimes:

I'm using the tikz package to create it. However, the indexes are not placed correctly:

I saw other similar questions, but it doesn't work properly in my case. Does anyone have a suggestion?

This can be achieved with a picture. The \sum symbol actually occupies 90% of its vertical size as stored in the bounding box.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}

\makeatletter
\DeclareRobustCommand{\dplus}{\DOTSB\mathop{\dplus@}\slimits@}
\newcommand{\dplus@}{\vphantom{\sum}\mathpalette\dplus@@\relax}
\newcommand{\dplus@@}[2]{%
\begingroup
\sbox\z@{$#1\sum$}%
\unitlength=\dimexpr\ht\z@+\dp\z@\relax
\linethickness{%
\ifx#1\displaystyle 1.8\fontdimen8\textfont3 \else
\ifx#1\textstyle 1.2\fontdimen8\textfont3 \else
\ifx#1\scriptstyle 1.2\fontdimen8\scriptfont3 \else
1.3\fontdimen8\scriptscriptfont3 \fi\fi\fi}
\vcenter{\hbox{%
\begin{picture}(1,1)
\polygon(0.05,0.5)(0.5,0.05)(0.95,0.5)(0.5,0.95)
\Line(0.5,0.05)(0.5,0.95)
\Line(0.05,0.5)(0.95,0.5)
\end{picture}%
}}%
\endgroup
}
\makeatother

\begin{document}

$\dplus_{n=1}^N \sum_{n=1}^N$
\begin{center}% for text style
$\dplus_{n=1}^N \sum_{n=1}^N$ \\
$\scriptstyle \dplus_{n=1}^N \sum_{n=1}^N$ \\
$\scriptscriptstyle \dplus_{n=1}^N \sum_{n=1}^N$
\end{center}

\end{document}


The parameter \fontdimen8 in the font of family 3 stores the default rule thickness for the current style (fraction line, overline, underline).