@**techreport**{RISC5946,author = {Mark van Hoeij and Cristian-Silviu Radu },

title = {{COMPUTING AN ORDER COMPLETE BASIS FOR M∞(N) AND APPLICATIONS}},

language = {english},

abstract = {This paper gives a quick way to construct all modular functions
for the group Γ0 (N ) having only a pole at τ = i∞. We assume that we are
given two modular functions f, g for Γ0 (N ) with poles only at i∞ and coprime
pole orders. As an application we obtain two new identities from which one can
derive that p(11n + 6) ≡ 0 (mod 11), here p(n) is the usual partition function.
},

number = {19-50},

year = {2019},

keywords = {integral bases, modular functions},

length = {6},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}