Lifting of Modular Forms
Jitendra Bajpai
Publications Mathématiques de Besançon no. 1  (2019), p. 5-20

The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group G, for any representation ρ:GGL d () of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup ker(ρ) of G. In this article vvmf are explicitly constructed for any admissible multiplier (representation) ρ, see Section 3 for the definition of admissible multiplier. In other words, the following question has been partially answered: For which representations ρ of a given G, is there a vvmf with at least one nonzero component?

L’existence et construction de formes modulaires vectorielles (vvmf) pour un groupe Fuchsien arbitraire G et pour une représentation ρ:GGL d () d’image finie peut être établie en relevant des formes modulaires scalaires pour le sous-groupe d’indice fini ker(ρ) de G. Dans cet article, des vvmf sont explicitement construites pour tout multiplicateur admissible (représentation) ρ (voir paragraphe 3 pour la définition du multiplicateur admissible). En d’autres termes, on a partiellement répondu à la question suivante : Pour quelles représentations ρ d’un groupe G donné, existe-t-il une vvmf avec au moins une composante non nulle ?

Received : 2017-06-03
Published online : 2019-10-15
Classification:  11F03,  11F55,  30F35
Keywords: Fuchsian group, Vector-valued modular form, Induced representation
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     author = {Jitendra Bajpai},
     title = {Lifting of Modular Forms},
     journal = {Publications Math\'ematiques de Besan\c con},
     publisher = {Presses universitaires de Franche-Comt\'e},
     number = {1},
     year = {2019},
     pages = {5-20},
     language = {en},
     url = {https://pmb.centre-mersenne.org/item/PMB_2019___1_5_0}
}
Bajpai, Jitendra. Lifting of Modular Forms. Publications Mathématiques de Besançon, no. 1 (2019), pp. 5-20. pmb.centre-mersenne.org/item/PMB_2019___1_5_0/

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