Glasnik Matematicki, Vol. 59, No. 2 (2024), 313-325. \( \)

POLYNOMIALS VANISHING ON A BASIS OF \(S_m(\Gamma_0(N))\)

Iva Kodrnja and Helena Koncul

Faculty of Geodesy, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:iva.kodrnja@geof.unizg.hr

Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:helena.koncul@grad.unizg.hr

Abstract.   In this paper we compute the bases of homogeneous polynomials of degree \(d\) such that they vanish on cuspidal modular forms of even weight \(m\geq 4\) that form a basis for \(S_m(\Gamma_0(N))\). Among them we find the irreducible ones.

2020 Mathematics Subject Classification.   11F11, 05E40, 13F20

Key words and phrases.   Modular forms, modular curves, projective curves, Hilbert polynomial

https://doi.org/10.3336/gm.59.2.04

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