A table of Hecke operators. II. (English) Zbl 0273.10019

Wada, Hideo

Proc. Japan Acad. 49, 380-384 (1973).

reducible factors) for (1) \(0<cq<250\), \(q \ne 227, 239\), (2) \(0<p<1000\), \(p\ne q\) and in this paper there is a list of \(F_{2,q}(x)\) and \(F_{3,q}\)(x). Let \(S'(q)\) be the set of cusp forms \(f(z)\) such that \[ f\left(\frac{az + b}{cz+d}\right) = \left(\frac{a}{q}\right)(cz+d)^2 f(z),\quad \left(\frac{a}{q}\right) = \text{ Legendre symbol},\quad \begin{pmatrix} a & b \\ c & d\end{pmatrix} \in\Gamma_0(q). \] In another paper [Tables of Hecke operators. I, Semin. Modern Methods Number Theory, Inst. Stat. Math., Tokyo 1971, 10 p. (1971; Zbl 0307.10029)], the author made a small table of Hecke operators \(T(p)\) which operate on \(S'(q)\).

Reviewer: Hideo Wada

MSC:

11F25	Hecke-Petersson operators, differential operators (one variable)
11F12	Automorphic forms, one variable

Keywords:

cusp forms; Hecke operators; table

Citations:

Zbl 0307.10029

References:

[1]	H. Wada: A Table of Hecke Operators. I. United States-Japan Seminar on Modern Methods in Number Theory, pp. 1-10 (1971). Tokyo University. · Zbl 0307.10029
[2]	H. Wada: On a Method of Calculations of Hecke Operators (in Japanese). Surikaiseki Kenkyujo Kokyuroku, No. 155, pp. 3-13.
[3]	H. G. Zimmer: Computational Problems, Methods, and Results in Algebraic Number Theory. Lecture Notes in Math. Vol. 262, Springer (1972). · Zbl 0231.12001