When you use the ModularForms constructor to create a space of modular 
forms, the backend computation of things like Hecke operators is carried 
out using the ModularSymbols class. Would it make sense to be able to 
provide the constructor with an optional argument specifying a different 
backend, such as one of the following? (ModularSymbols would remain as the 
default.)

-- CremonaModularSymbols is a separate implementation of modular symbols 
derived from Cremona's code for tabulating modular elliptic curves.
-- BrandtModules implements the "method of graphs" operating on ideal 
classes in a quaternionic order.
-- Pari recently added a "method of trace formulas".
-- Possibly coming soon: Birch's variant of the method of graphs based on 
reduction of quadratic forms (see https://trac.sagemath.org/ticket/23342).
-- Did I miss something obvious?

There are plenty of caveats here. For one, these methods don't all apply at 
the same level of generality, or offer the same feature set even in cases 
of overlapping applicability. For another, some of these methods are 
working with different constructions that produce isomorphic Hecke modules, 
but not "the same" (i.e., not canonically isomorphic) underlying spaces.

Kiran

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