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Let f_i be an infinite sequence of elliptic Hecke eigenforms such that the individual weights and levels are unbounded as i goes to infinity. When does one expect that f_i's have a common zero? Any guess basesbased on heuristics/ conjectures is welcome! Any non-trivial example of this phenoemena?

Let f_i be an infinite sequence of elliptic Hecke eigenforms such that the individual weights and levels are unbounded. When does one expect that f_i's have a common zero? Any guess bases on heuristics/ conjectures is welcome! Any non-trivial example of this phenoemena?

Let f_i be an infinite sequence of elliptic Hecke eigenforms such that the individual weights and levels are unbounded as i goes to infinity. When does one expect that f_i's have a common zero? Any guess based on heuristics/ conjectures is welcome! Any non-trivial example of this phenoemena?

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Common zeros of modular forms

Let f_i be an infinite sequence of elliptic Hecke eigenforms such that the individual weights and levels are unbounded. When does one expect that f_i's have a common zero? Any guess bases on heuristics/ conjectures is welcome! Any non-trivial example of this phenoemena?