Definition 8.6.1 (Manin constant)
The Manin constant of
is the index in its saturation of
in
under the appropriate natural identifications
(see [ARS06]).

Problem 8.6.2
Find (and implement) an algorithm to compute the prime
divisors of the Manin constant of
.

This is closely related to understanding
-expansions at cusps
other than
.

Problem 8.6.3
Give a modular form
compute
the
-expansion of
at all the cusps.

Remark 8.6.4 (From John Cremona:)
Prob 8.6.3 was dealt with in Delaunay's thesis.

Problem 8.6.5
Implement in SAGE Delaunay's algorithm to compute the
-expansion
of a modular form at all cusps.

Problem 8.6.6
Give a modular form
compute
the
-expansion of
at all the cusps.