Alternate Ways of Writing Complex Summations

In my writing, I often have to consider summation formulas where describing the terms of the summation make the equation rather weirdly spaced out. For instance, I am currently considering the formula

$$\sum_{J_1, \dots, J_n \in \mathcal{B}^d_l(E)} \sum_{K \in \mathcal{B}^{dn}_l(G) \cap \mathcal{B}^{dn}_s(J_1 \times \dots \times J_n)} \prod_{i = 1}^n \mathbf{I}(I_{J_i} = K_i).$$

Are there any alternate ways of writing these kinds of formulae, stylewise, which makes the equation look more pleasant. Something really annoys me about the spacing between the different $$\Sigma$$'s.

• This is maybe not optimal, but already an improvement: $$\sum_{\substack{J_i,\ldots,J_n\in\mathcal{B}_l^d(E)\\K\in\mathcal{B}^{dn}_l(G)\cap\mathcal{B}^{dn}_s(J_1\times\cdots\times J_n)}}\prod_{i=1}^n\mathbf{I}(I_{J_i}=K)$$ This question should be moved to TeX.SE though... – Daniel Robert-Nicoud May 22 at 17:56
• or with $J=(J_1,\dots,J_n)$, $$\sum_{J \in \mathcal{B}^d_l(E)^n\atop K \in \mathcal{B}^{dn}_l(G) \cap \mathcal{B}^{dn}_s(\prod_i J_i)} \prod_{i = 1}^n\; \mathbf{I}(I_{J_i} = K_i).$$ – Pietro Majer May 22 at 18:00
• You can leave only $K$ and $J$ under the summation signs, and explain their range is a separate line, in a separate sentence, "Where the summation is over $J\in...$ and $K\in...$." – Alexandre Eremenko May 22 at 18:25
• @Yemon, it's not really about TeX, as Alexandre's comment shows. – Gerry Myerson May 22 at 23:06
• @GerryMyerson Fair point. Since I can't undo my vote to close (AFAIK) I'll just leave this acknowledgment here – Yemon Choi May 23 at 1:18