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# The Manin constant

Let be a quotient of .

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.

William Stein 2006-10-20