# Computing classical modular forms

@article{Best2020ComputingCM, title={Computing classical modular forms}, author={Alex J Best and Jonathan W. Bober and Andrew R. Booker and Edgar Costa and John Cremona and Maarten Derickx and David Lowry-Duda and Min Lee and David Roe and Andrew V. Sutherland and John Voight}, journal={arXiv: Number Theory}, year={2020} }

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).

#### 3 Citations

Computing Classical Modular Forms for Arbitrary Congruence Subgroups.

- Mathematics
- 2020

In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $\Gamma$, where $\Gamma \subseteq SL_{2}({\mathbb{Z}})$… Expand

Twist-minimal trace formula for holomorphic cusp forms

- Mathematics
- 2021

We derive an explicit formula for the trace of an arbitrary Hecke operator on spaces of twist-minimal holomorphic cusp forms with arbitrary level and character, and weight at least 2. We show that… Expand

Computing newforms using supersingular isogeny graphs.

- Mathematics
- 2020

We describe an algorithm that we used to compute the $q$-expansions of all weight 2 cusp forms of prime level at most 800,000 and dimension at most 6. We also present an algorithm that we used to… Expand

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