Eta Quotients of Level $32$ and Weight $1$: Classification and Applications
Resumen
We find all the eta quotients in the spaces $M_{1}\left(\Gamma_{0}(32), \left(\frac{d}{*}\right)\right)$ with $d = -4, -8$ of modular forms,and we determine their Fourier coefficients, where $\left(\frac{d}{*}\right)$ is the Legendre-Jacobi-Kronecker symbol in the group of Dirichlet
characters modulo $32$ with values in the rational field $\mathbb{Q}$.
Descargas
La descarga de datos todavía no está disponible.
Citas
\bibitem{Diamond} F. Diamond and J. M. Shurman,
{\it A first course in modular forms}. Grad. Texts in Math., Springer, New York, (2005).
\bibitem{Gordon} B. Gordon and D. Sinor,
{\it Multiplicative properties of $\eta$-products}. In Number Theory, Madras 1987: Proceedings of the International Ramanujan Centenary Conference held at Anna University, Madras, India, Dec. 21, 1987, Springer, Berlin, Heidelberg, 173--200, (2006). https://doi.org/10.1007/BFb0086404
\bibitem{Kilford} L. J. P. Kilford,
{\it Modular forms: A classical and computational introduction}. 2nd ed., Imperial College Press, London, (2015).
\bibitem{Kohler} G. K\"{o}hler,
{\it Eta products and theta series identities}. Springer Monogr. Math., Springer, New York, (2011). https://doi.org/10.1007/978-3-642-16152-0
\bibitem{Ligozat} G. Ligozat,
{\it Courbes modulaires de genre $1$}. Bull. Soc. Math. France {\bf 43}, 5--80, (1975). http://eudml.org/doc/94716
\bibitem{Okamoto} A. Okamoto,
{\it On expressions of theta series by $\eta$-products}. Tokyo J. Math. {\bf 34}(2), 319--326, (2011). https://doi.org/10.3836/tjm/1327931388
\bibitem{Stein} W. A. Stein,
{\it Modular forms, a computational approach}. Grad. Stud. Math., Vol. 79, Amer. Math. Soc., Providence, RI, (2007). http://dx.doi.org/10.1090/gsm/079
\bibitem{bib7} W. A. Stein et al.,
{\it Sage Mathematics Software (Version 10.4)}. The Sage Development Team, (2023). http://www.sagemath.org/
\bibitem{Williams} K. S. Williams,
{\it Fourier series of a class of eta quotients}. Int. J. Number Theory {\bf 8}(4), 993--1004, (2012). https://doi.org/10.1142/S1793042112500595
{\it A first course in modular forms}. Grad. Texts in Math., Springer, New York, (2005).
\bibitem{Gordon} B. Gordon and D. Sinor,
{\it Multiplicative properties of $\eta$-products}. In Number Theory, Madras 1987: Proceedings of the International Ramanujan Centenary Conference held at Anna University, Madras, India, Dec. 21, 1987, Springer, Berlin, Heidelberg, 173--200, (2006). https://doi.org/10.1007/BFb0086404
\bibitem{Kilford} L. J. P. Kilford,
{\it Modular forms: A classical and computational introduction}. 2nd ed., Imperial College Press, London, (2015).
\bibitem{Kohler} G. K\"{o}hler,
{\it Eta products and theta series identities}. Springer Monogr. Math., Springer, New York, (2011). https://doi.org/10.1007/978-3-642-16152-0
\bibitem{Ligozat} G. Ligozat,
{\it Courbes modulaires de genre $1$}. Bull. Soc. Math. France {\bf 43}, 5--80, (1975). http://eudml.org/doc/94716
\bibitem{Okamoto} A. Okamoto,
{\it On expressions of theta series by $\eta$-products}. Tokyo J. Math. {\bf 34}(2), 319--326, (2011). https://doi.org/10.3836/tjm/1327931388
\bibitem{Stein} W. A. Stein,
{\it Modular forms, a computational approach}. Grad. Stud. Math., Vol. 79, Amer. Math. Soc., Providence, RI, (2007). http://dx.doi.org/10.1090/gsm/079
\bibitem{bib7} W. A. Stein et al.,
{\it Sage Mathematics Software (Version 10.4)}. The Sage Development Team, (2023). http://www.sagemath.org/
\bibitem{Williams} K. S. Williams,
{\it Fourier series of a class of eta quotients}. Int. J. Number Theory {\bf 8}(4), 993--1004, (2012). https://doi.org/10.1142/S1793042112500595
Publicado
2026-02-23
Sección
Conf. Issue: Advances in Algebra, Analysis, Optimization, and Modeling
Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
