THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4)