Moved to sage: http://trac.sagemath.org/ticket/16134

At the moment: Only support for forms with respect to the full Hecke triangle group for n=3, 4, 5, ...

The ring of modular forms as a commutative algebra.

The space of modular forms of given weight as a module.

Supported analytic types (implemented as an extended FiniteLatticePoset class):

• meromorphic
• weakly holomorphic
• holomorphic
• cuspidal
• Support for quasi modular forms for all of the above types

Exact calculations (no precision argument is required).

The calculations are based on the three generators of the graded algebra: x=f_rho, y=f_i, z=E2. Every form has a representation as a rational function in x, y, z.

Checks are performed to determine the analytic type of elements.

Fourier expansion with (exact) coefficients in Frac(R)[d], where R is some base ring (e.g. ZZ) and d is a formal parameter corresponding to a (possibly) transcendental number which turns up in the Fourier expansion.

It is also possible to evaluate d numerically.

The Fourier expansion is (should be) determined exactly with the specified precision.

For arithmetic groups the d is calculated exactly.

Evaluation of elements, viewed as functions from the upper half plane. This uses the modularity properties for faster/more precise evaluation. However the precision of the result depends on the precision specified for the Fourier expansion.

Calculation of derivatives and serre derivatives.

Basis for weakly holomorphic modular forms.

Faber polynomials.

(Exactly) determine weakly holomorphic modular forms by their initial Fourier coefficients.

Dimension and basis for holomorphic or cuspidal (quasi) modular forms.

Coordinate vectors for holomorphic modular forms and cusp forms.

Subspaces (with respect to a basis) for ambient spaces that support coordinate vectors, together with coordinate vectors for subspaces.

Complete documentation of all functions and methods.

Complete doctests of all functions and methods.