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.