Abstract
We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when <TEX>$K_{(2p)}$</TEX> denotes the ray class field of <TEX>$K=\mathbb{Q}(e^{2{\pi}i/5})$</TEX> modulo 2p for an odd prime p, we describe a subfield of <TEX>$K_{(2p)}$</TEX> generated by the special value of a certain theta constant by using Shimura's reciprocity law.
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