We have performed replica-exchange molecular dynamics (REMD) simulations on the dimer formation of fibrilforming segments of $alpha$-Synuclein (residues 71 - 82) using implicit solvation models with two kinds of force fields- AMBER parm99SB and parm96. We observed spontaneous formation of dimers from the extensive simulations, demonstrating the self-aggregating and fibril forming properties of the peptides. Secondary structure profile and clustering analysis showed that dimers with antiparallel $eta$-sheet conformations, stabilized by well-defined hydrogen boding, are major species corresponding to global free energy minimum. Parallel dimers with partial $eta$-sheets are found to be off-pathway intermediates. The relative instability of the parallel arrangements is due to the repulsive interactions between bulky and polar side chains as well as weaker backbone hydrogen bonds.