# Approximating *V*_{f} over the complex numbers

_{f}

# Approximating *V*_{f} over the complex numbers

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This chapter addresses the problem of computing torsion divisors on modular curves with an application to the explicit calculation of modular representations. The final result of the chapter is Theorem 12.14.1 (approximating *V*subscript *f*). It identifies two differences between this Theorem 12.14.1 and Theorem 12.10.7. First, it claims that it can separate the cuspidal and the finite part of *Q*ₓ. Second, it returns algebraic coordinates *b* and *x* for the points *Q*subscript *x,n* rather than analytic ones.

*Keywords:*
modular forms, torsion divisors, modular curves, modular representation

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