Paramodular forms coming from elliptic curves
نویسندگان
چکیده
There is a lifting from non-CM elliptic curve $E/\mathbb{Q}$ to paramodular form $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find level in an explicit way terms coefficients Weierstrass equation $E$. In order compute level, we use available description local representations $\mathrm{GL}(2,\mathbb{Q}_p)$ attached $E$ for $p \ge 5$ determine representation $\mathrm{GL}(2,\mathbb{Q}_3)$
منابع مشابه
Elliptic Curves and Modular Forms
This is an exposition of some of the main features of the theory of elliptic curves and modular forms.
متن کاملPacket structure and paramodular forms
We explore the consequences of the structure of the discrete automorphic spectrum of the split orthogonal group SO(5) for holomorphic Siegel modular forms of degree 2. In particular, the combination of the local and global packet structure with the local paramodular newform theory for GSp(4) leads to a strong multiplicity one theorem for paramodular cusp forms.
متن کاملELLIPTIC CURVES AND MODULAR FORMS Contents
1. January 21, 2010 2 1.1. Why define a curve to be f rather than V (f) ⊂ P(k)? 3 1.2. Cubic plane curves 3 2. January 26, 2010 4 2.1. A little bit about smoothness 4 2.2. Weierstrass form 5 3. January 28, 2010 6 3.1. An algebro-geometric description of the group law in terms of divisors 6 3.2. Why are the two group laws the same? 7 4. February 2, 2010 7 4.1. Overview 7 4.2. Uniqueness of Weier...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2021.06.007