subject:(symmetric cube lifting)

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University of Oklahoma

1. Roy, Manami. ELLIPTIC CURVES AND PARAMODULAR FORMS.

Degree: PhD, 2019, University of Oklahoma

URL: http://hdl.handle.net/11244/321046

There is a lifting from a non-CM elliptic curve E/ℚ to a cuspidal paramodular newform f of degree 2 and weight 3 given by the symmetric cube map. We find a description of the level of f in terms of the coefficients of the Weierstrass equation of E. In order to compute the paramodular level, we need a detailed description of the local representations π_p of \GL(2,ℚ_p) attached to E/ℚ_p, where π\cong\bigotimes\limits_pπ_p is the cuspidal automorphic representation of \GL(2,\mathbb{A}_ℚ) associated with E/ℚ. We use the available description of the local representations of \GL(2,ℚ_p) attached to E for p ≥ 5 and determine the local representation of \GL(2,ℚ₃) attached to E. In fact, we study the representations of \GL(2, K) attached to E/K for any non-archimedean local field K of characteristic 0 and residue characteristic 3. Advisors/Committee Members: Schmidt, Ralf (advisor), Dunn, Anne (committee member), Lifschitz, Lucy (committee member), Pitale, Ameya (committee member), Roche, Alan (committee member).

Subjects/Keywords: elliptic curves; paramodular forms; symmetric cube lifting

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APA (6^th Edition):

Roy, M. (2019). ELLIPTIC CURVES AND PARAMODULAR FORMS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/321046

Chicago Manual of Style (16^th Edition):

Roy, Manami. “ELLIPTIC CURVES AND PARAMODULAR FORMS.” 2019. Doctoral Dissertation, University of Oklahoma. Accessed January 23, 2021. http://hdl.handle.net/11244/321046.

MLA Handbook (7^th Edition):

Roy, Manami. “ELLIPTIC CURVES AND PARAMODULAR FORMS.” 2019. Web. 23 Jan 2021.

Vancouver:

Roy M. ELLIPTIC CURVES AND PARAMODULAR FORMS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2019. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/11244/321046.

Council of Science Editors:

Roy M. ELLIPTIC CURVES AND PARAMODULAR FORMS. [Doctoral Dissertation]. University of Oklahoma; 2019. Available from: http://hdl.handle.net/11244/321046

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