Given the first 6 terms of a Fourier series expansion, is there a cusp form of weight 50 whose Fourier expansion begins that way

Question

Is there a cusp form of weight 50 whose Fourier expansion begins with.. the first 6 terms being $q + 13q^2 + 611q^3 − 6546q^4 + 17727398783055q^5 + 5003897687242243q^6$. My guess is that I am supposed to use the fact that the coefficients of cusp form of weight 2k satisfy $a_n = O(n^k)$, but I am unsure how to actually use this.