An analogue of Sturm's theorem for Hilbert modular forms

作者：Takai Yuuki^*

来源：Algebra and Number Theory, 2013, 7(4): 1001-1018.

DOI：10.2140/ant.2013.7.1001

• Hilbert modular forms and varieties
• congruences of modular forms
• Sturm's theorem
• toroidal and minimal compactifications
• intersection numbers

In this paper, we consider congruences of Hilbert modular forms. Sturm showed that mod l elliptic modular forms of weight k and level Gamma(1) (N) are determined by the first (k/12) [Gamma(1) (1) : Gamma(N)] mod l Fourier coefficients. We prove an analogue of Sturm's result for Hilbert modular forms associated to totally real number fields. The proof uses the positivity of ample line bundles on toroidal compactifications of Hilbert modular varieties.

• 出版日期2013