1. A short note on inadmissible coefficients of weight 2 and $$2k+1$$ newforms
- Author
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Andreas Hatziiliou and Malik Amir
- Subjects
Mathematics::Number Theory ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,Congruence relation ,Galois module ,01 natural sciences ,Dirichlet character ,Prime (order theory) ,Ramanujan's sum ,Combinatorics ,Elliptic curve ,symbols.namesake ,Number theory ,Integer ,010201 computation theory & mathematics ,symbols ,0101 mathematics ,Mathematics - Abstract
Let$$f(z)=q+\sum _{n\ge 2}a(n)q^n$$f(z)=q+∑n≥2a(n)qnbe a weightknormalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, Ramanujan J, 2021) for$$k=2$$k=2by ruling out or locating all odd prime values$$|\ell ||ℓ|<100of their Fourier coefficientsa(n) whennsatisfies some congruences. We also study the case of odd weights$$k\ge 1$$k≥1newforms where the nebentypus is given by a quadratic Dirichlet character.
- Published
- 2021