Ongoing work on the LMFDB will add more data, include more mathematical objects, provide better searching and browsing, and give more detailed information about each object in the database. The lists below describe some of the planned enhancements. To make comments or suggestions about the future of LMFDB, please use the Feedback form available at the top of every page.

L-functions

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Available data

Add the L-functions of: Maass forms (some currently limited by the number of available coefficients), $sym^2$ of CM elliptic curves, $sym^2$ of other GL(2) objects, Siegel modular forms, Hilbert modular forms (Asai L-function), Artin representations.

Elliptic modular forms

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Available data

Elliptic Curves

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Additional data

Elliptic curves over number fields

Dirichlet characters

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Available data

Hilbert modular forms

Approximately 240000 forms are available over totally real fields of degree up to 6.

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Available Data

Technical Issues

Possible new subcategories

Maass forms

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Available Data

Technical Issues

Possible new subcategories

Siegel Modular Forms

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Database

Artin representations

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The search page will be expanded to include searches based on information depending on the Artin field (for instance the Galois group).

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Available data

Very limited data is available right now (37000 representations). We will soon add more data, coming from computations of Tim Dokchitser.

Global number fields

Currently have fields with small absolute discriminant in degrees $\leq 11$, and other complete sets of fields with degrees up to $15$. See completeness of global number field data for more details

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Local number fields

Currently have all degree $n$ fields over $\mathbb{Q}_p$ for $p<150$ and $1\leq n\leq11$.

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Give components of interesting local resolvent algebras, such as twins for sextics and $D_4$ quartics

Available data

Galois groups

Currently the database contains all transitive subgroups of $S_n$ up to conjugation for $n\leq 23$.

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Future areas

Objects which will be added to the LMFDB include: