On the moduli of convexity

It is known that, given a Banach space $(X,\Vert\cdot\Vert)$, the modulus of convexity associated to this space $\delta_X$ is a non-negative function, non-decreasing, bounded above by the modulus of convexity of any Hilbert space and satisfies the equation $\frac{\delta_X(\varepsilon)}{\varepsilon^2}\leq 4L\frac{\delta_X(\mu)}{\mu^2}$ for every $0<\varepsilon\leq\mu\leq 2$, where $L>0$ is a constant. We show that, given a function $f$ satisfying these properties then, there exists a Banach space in such a way its modulus of convexity is equivalent to $f$, in Figiel's sense. Moreover this Banach space can be taken to be two-dimensional.