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We define an effective divisor of the moduli space of stable curves$\overline{M_g}$, which is denoted $\overline{S^{2}W}$. Writing the class of$\overline{S^{2}W}$ in the Picard group of the moduli functorPic$_{\text{fun}}(\overline{M_{g}})\otimes \mathbb{Q}$ in terms of theso-called Harer basis $\lambda,\delta_0,\ldots,\delta_{[g/2]}$, we prove thatthe relations among the coefficients of $\delta_1,\ldots,\delta_{[g/2]}$ arethe same relations on coefficients as the Brill-Noether divisors. We present aresult on effective divisors of $\overline{M_g}$ which could be useful to getthe same relations on coefficients for other divisors. We also compute thecoefficient of $\lambda$.

An Effective Divisor in $\overline{M_{g}}$ Defined by Ramification Conditions