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arXiv · 1707.01693

Indecomposable vector-valued modular forms and periods of modular curves

Luca Candelori·Tucker Hartland·Christopher Marks·Diego Yepez
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Abstract

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be employed to compute periods of modular curves. This technique obviates the use of Hecke operators, and therefore provides a method for studying noncongruence modular curves as well as congruence.

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Luca Candelori, Tucker Hartland, Christopher Marks, Diego Yepez. 2017-07-06. Indecomposable vector-valued modular forms and periods of modular curves. https://arxiv.org/abs/1707.01693

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