Differential equations for septic theta functions

Balanced Modular Parameterizations

“…For example, the Hecke Eisenstein series twisted, respectively by the Jacobi symbol and trivial character χ 1,7 modulo seven have the symmetric representations [10,21] x…”

“…Each system is invariant under action by Γ 0 (p). The differential systems of level five and seven appeared recently in [20,21]. Their coefficient invariance is a common feature of the coupled differential systems derived for each set of generators of level 5 ≤ p ≤ 19.…”