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Let S(k +1 /2 ,N , χ) denote the space of cusp forms of weight k +1 /2, level N , and character χ .L etRψ be a twisting operator for a quadratic primitive character ψ of even conductor and ˜ T (n 2 )t hen 2 -th Hecke operator. We give an explicit trace formula of Rψ ˜ T (n 2 )o n S(k +1 /2 ,N , χ).

Trace formula of twisting operators of half-integral weight in the case of even conductors