We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic nonlinear Schrödinger equation in the modulation space $$M_{p,q}^{s}({\mathbb {R}})$$ M p , q s ( R ) where $$1\le q\le 2$$ 1 ≤ q ≤ 2 , $$2\le p<\frac{10q'}{q'+6}$$ 2 ≤ p < 10 q ′ q ′ + 6 and $$s\ge 0$$ s ≥ 0 . Moreover, for either $$1\le q\le \frac{3}{2}, s\ge 0$$ 1 ≤ q ≤ 3 2 , s ≥ 0 and $$2\le p\le 3$$ 2 ≤ p ≤ 3 or $$\frac{3}{2}<q\le \frac{18}{11}, s>\frac{2}{3}-\frac{1}{q}$$ 3 2 < q ≤ 18 11 , s > 2 3 - 1 q and $$2\le p\le 3$$ 2 ≤ p ≤ 3 or $$\frac{18}{11}<q\le 2, s>\frac{2}{3}-\frac{1}{q}$$ 18 11 < q ≤ 2 , s > 2 3 - 1 q and $$2\le p<\frac{10q'}{q'+6}$$ 2 ≤ p < 10 q ′ q ′ + 6 we show that the Cauchy problem is unconditionally wellposed in $$M_{p,q}^{s}({\mathbb R}).$$ M p , q s ( R ) . This improves Pattakos (J Fourier Anal Appl, 2018. https://doi.org/10.1007/s00041-018-09655-9 ), where the case $$p=2$$ p = 2 was considered and the differentiation-by-parts technique was introduced to a problem with continuous Fourier variable. Here, the same technique is used, but more delicate estimates are necessary for $$p\ne 2$$ p ≠ 2 .