How to check if 2 eigenforms are equal?

[Jared Weinstein]

Hello,

Suppose f and g are *eigenforms* in some common space of modular
forms. How many coefficients of f and g must agree before one can
prove that f = g? Is it necessary to check up to the Sturm bound for
the space?

Jared

[William Stein]

One can sometimes do better for eigenforms. This is addressed in
Sturm's paper where he deduces one special case. Also, Kevin Buzzard
and I wrote a paper where we also needed something better than Sturm's
bound, and we deduced something better: See
http://wstein.org/papers/artin/

William