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arXiv · 0905.2887

Explicit Computation of Cusp forms via Hecke Action on Cohomology and its Complexity

Jonas B. Rasmussen
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Abstract

In the literature, the standard approach to finding bases of spaces of modular forms is via modular symbols and the homology of modular curves. By using the Eichler-Shimura isomorphism, a work by Wang shows how one can use a cohomological viewpoint to determine bases of spaces of cusp forms on $Γ_0(N)$ of weight $k \geq 2$ and character $χ$. It is interesting to look at the complexity of this alternative approach, and we do this for an explicit implementation of the algorithm suggested by Wang.

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Jonas B. Rasmussen. 2009-05-18. Explicit Computation of Cusp forms via Hecke Action on Cohomology and its Complexity. https://arxiv.org/abs/0905.2887

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