initial version

src/sage/modular/hecke_mf/.gitignore

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+TODO
+clean.sh
+test.sage
+
+*.py[cod]
+*~

src/sage/modular/hecke_mf/README

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+Hecke modular forms
+===================
+
+  * Trac ticket: 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.
+
+
+
+Future ideas (hard):
+--------------------
+
+  * Support for general triangle groups
+  * Support for "congruence" subgroups