OEIS A000114: Number of cusps of principal congruence subgroups

We journey from the simple counting sequence A000114 to the geometry of modular surfaces formed by principal congruence subgroups of SL(2,Z). See how the number of cusps, dictated by the level, shapes the quotient space, influences modular forms, and connects to related ideas like Heck congruence subgroups — a compact tour of how group theory, hyperbolic geometry, and arithmetic meet around this OEIS entry.

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