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Modular supercuspidal lifts of weight 2.

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Title: Modular supercuspidal lifts of weight 2.
Authors: Blanco-Chacón, Iván1 (AUTHOR) ivan.blancoc@uah.es, Dieulefait, Luis2 (AUTHOR) ldieulefait@ub.edu
Source: Journal of Number Theory. Aug2026, Vol. 285, p54-73. 20p.
Subjects: Modular forms, Number theory, Representation theory
Abstract: Let F / Q be a totally real number field and N an ideal of its ring of integers of norm N. Let p > max ⁡ { k + 1 , 6 } be a prime totally split in F such that p ∤ N. For every even k ≥ 2 , define the [ F : Q ] -dimensional parallel weight k = (k ,... , k). Let f ∈ S k (Γ 0 (N)) be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation ρ ‾ f , P has large image for some prime P over p in the field of definition of f. Under these conditions, we prove that there exists a lift of ρ ‾ f , P associated to a Hilbert modular cuspform g ∈ S 2 (N p 2 , ϵ) which is supercuspidal at each prime of F over p. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare [23] with classical techniques. Finally, using our main result we give a corrigenda for [12] , correctly inserting the micro good dihedral prime in the level. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192176187
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  Data: Modular supercuspidal lifts of weight 2.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Aug2026, Vol. 285, p54-73. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Modular+forms%22">Modular forms</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Representation+theory%22">Representation theory</searchLink>
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  Data: Let F / Q be a totally real number field and N an ideal of its ring of integers of norm N. Let p > max ⁡ { k + 1 , 6 } be a prime totally split in F such that p ∤ N. For every even k ≥ 2 , define the [ F : Q ] -dimensional parallel weight k = (k ,... , k). Let f ∈ S k (Γ 0 (N)) be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation ρ ‾ f , P has large image for some prime P over p in the field of definition of f. Under these conditions, we prove that there exists a lift of ρ ‾ f , P associated to a Hilbert modular cuspform g ∈ S 2 (N p 2 , ϵ) which is supercuspidal at each prime of F over p. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare [23] with classical techniques. Finally, using our main result we give a corrigenda for [12] , correctly inserting the micro good dihedral prime in the level. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jnt.2025.12.015
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 54
    Subjects:
      – SubjectFull: Modular forms
        Type: general
      – SubjectFull: Number theory
        Type: general
      – SubjectFull: Representation theory
        Type: general
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      – TitleFull: Modular supercuspidal lifts of weight 2.
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            NameFull: Blanco-Chacón, Iván
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            NameFull: Dieulefait, Luis
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              Text: Aug2026
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              Y: 2026
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              Value: 285
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