Summary: Let \(g\) be a non-zero rapidly decreasing function and \(w\) be a weight function. In this article, in analogy to the modulation space, we define the space \(M (p,q,w) (\mathbb R^d)\) to be the subspace of tempered distributions \(f\in {\mathcal S}' (\mathbb R^d)\) such that the Gabor transform \(V_g (f)\) of \(f\) is in the weighted Lorentz space \(L (p, q, w\text{d}\mu) (\mathbb R^{2d})\). We endow this space with a suitable norm and show that it becomes a Banach space and is invariant under time frequency shifts for \(1\leq p, q\leq \infty\). We also investigate the embeddings between these spaces and the dual space of \(M (p,q,w) (\mathbb R^d)\). Later, we define the space \(S (p,q,r,w,\omega) (\mathbb R^d)\) for \(1<p<\infty, 1\leq q\leq \infty\). We endow it with a sum norm and show that it becomes a Banach convolution algebra. We also discuss some properties of \(S (p,q,r,w,\omega) (\mathbb R^d)\). At the end of this article, we characterize the multipliers of the spaces \(M (p,q,w) (\mathbb R^d)\) and \(S (p,q,r,w,\omega) (\mathbb R^d)\).