A problem which has received a lot of attention in the area of analytic number theory is the subconvexity problem. Let \(L(f,s)\) be an automorphic \(L\)-function and \(s\in C\) with \(\Re(s)=\frac{1}{2}\), then a subconvexity bound would be a bound of the form \(L(f,s)\ll \mathcal{Q}(f,s)^{1/4-\delta+\epsilon}\) for some \(\delta>0\), where \(\mathcal{Q}(f,s)\) is the analytic conductor of the \(L\)-function at \(s\).

By looking into the direct applications of the delta method developed by Duke, Friedlander and Iwaniec, we explore new methods to attain subconvexity bounds for \(L\)-functions. We focus mainly on the \(GL(2)\) \(L\)-functions and their twists in the level aspect. Motivated by the challenge of R. Munshi, to establish \(GL(2)\) level aspect subconvexity without appealing to moments, we establish a subconvexity result for \(GL(2)\times GL(1)\) \(L\)- functions in the hybrid level aspect.