  Suppose \( \rho_1 \) and \( \rho_2 \) are two pure Galois representations of
the absolute Galois group of a number field $K$ of weights \( k_1 \) and \( k_2
\) respectively, having equal normalized Frobenius traces \(
Tr(\rho_1(\sigma_v)) /Nv^{k_1/2}\) and \( Tr(\rho_2(\sigma_v)) /Nv^{k_2/2}\) at
a set of primes \( v\) of $K$ with positive upper density. Assume further that
the algebraic monodromy group of $\rho_1$ is connected and the repesentation is
absolutely irreducible. We prove that \( \rho_1 \) and \( \rho_2 \) are twists
of each other by power of a Tate twist times a character of finite order.
  We apply this to modular forms and deduce a result proved by Murty and
Pujahari.
