The modular trace of the normalized Hauptmodul has been extended to the Galois trace of a class invariant by Kaneko. It is an important issue to search for class invariants for which the Galois traces have modular properties. The crucial point in this paper is that we initiate a new notion, called Siegel resolvents; we define the Siegel resolvents as the quadratic polynomials of Siegel functions of level 3, so that they are modular functions of level 3 as well. We construct real-valued class invariants over imaginary quadratic fields by using the singular values of Siegel resolvents at imaginary quadratic irrationals. We also prove that the generating series of their Galois traces become a weakly holomorphic modular form with weight 3/2. This shows that the work of D. Zagier on traces of singular moduli can be extended to the modular functions of higher level.

归一化的Hauptmodul的模块化迹线已由Kaneko扩展到一类不变的Galois迹线。搜索Galois迹线具有模块属性的类不变量是一个重要的问题。本文的关键点是我们提出了一个新的概念，即Siegel解决方案; 我们将Siegel分解体定义为3级Siegel函数的二次多项式，因此它们也是3级的模函数。我们通过使用虚数二次无理值处的Siegel解析子的奇异值，在虚数二次域上构造实值类不变量。我们还证明了它们的伽罗瓦迹线的生成系列成为权重为3/2的弱全纯模形式。这表明D. Zagier在奇异模量迹上的工作可以扩展到更高级别的模块化功能。