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We improve the Chebotarev variant of the Brun-Titchmarsh theorem proven byLagarias, Montgomery, and Odlyzko using the log-free zero density estimate andzero repulsion phenomenon for Hecke L-functions that were recently proved bythe authors. Our result produces an improvement for the best unconditionalbounds toward two conjectures of Lang and Trotter regarding the distribution oftraces of Frobenius for elliptic curves and holomorphic cuspidal modular forms.We also obtain new results on the distribution of primes represented bypositive-definite integral binary quadratic forms.

A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures