  The well-known modular property of the torus characters and torus partition
functions of (rational) vertex operator algebras (VOAs) and 2d conformal field
theories (CFTs) has been an invaluable tool for studying this class of
theories. In this work we prove that sphere four-point chiral blocks of
rational VOAs are vector-valued modular forms for the groups $\Gamma(2)$,
$\Gamma_0(2)$, or $\text{SL}_2(\mathbb{Z})$. Moreover, we prove that the
four-point correlators, combining the holomorphic and anti-holomorphic chiral
blocks, are modular invariant. In particular, in this language the crossing
symmetries are simply modular symmetries. This gives the possibility of
exploiting the available techniques and knowledge about modular forms to
determine or constrain the physically interesting quantities such as chiral
blocks and fusion coefficients, which we illustrate with a few examples. We
also highlight the existence of a sphere-torus correspondence equating the
sphere quantities of certain theories $\mathcal{T}_s$ with the torus quantities
of another family of theories $\mathcal{T}_t$. A companion paper will delve
into more examples and explore more systematically this sphere-torus duality.
