scholarly journals Congruences between cusp forms and the geometry of Jacobians of modular curves

1993 ◽  
Vol 295 (1) ◽  
pp. 111-133 ◽  
Author(s):  
San Ling
Keyword(s):  
Cusp Forms ◽  
Modular Curves

scholarly journals Computing models for quotients of modular curves

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
Josha Box
Keyword(s):  
Automorphism Group ◽  
Cusp Forms ◽  
Modular Curves ◽  
Rational Model ◽  
Modular Curve ◽  
Space Of Cusp Forms ◽  
Computing Models

AbstractWe describe an algorithm for computing a $${\mathbb {Q}}$$ Q -rational model for the quotient of a modular curve by an automorphism group, under mild assumptions on the curve and the automorphisms, by determining q-expansions for a basis of the corresponding space of cusp forms. We also give a moduli interpretation for general morphisms between modular curves.

Modular symbols for 1(N) and elliptic curves with everywhere good reduction

1992 ◽  
Vol 111 (2) ◽  
pp. 199-218 ◽  
Author(s):  
J. E. Cremona
Keyword(s):  
Elliptic Curves ◽  
Quadratic Fields ◽  
Cusp Forms ◽  
Modular Curves ◽  
Good Reduction ◽  
Modular Symbols ◽  
Real Quadratic Fields ◽  
Real Quadratic

AbstractThe modular symbols method developed by the author in 4 for the computation of cusp forms for 0(N) and related elliptic curves is here extended to 1(N). Two applications are given: the verification of a conjecture of Stevens 14 on modular curves parametrized by 1(N); and the study of certain elliptic curves with everywhere good reduction over real quadratic fields of prime discriminant, introduced by Shimura and related to Pinch's thesis 10.

Congruences between Hilbert Cusp Forms

2018 ◽  
Author(s):  
Hiroshi Saito ◽  
Masatoshi Yamauchi
Keyword(s):  
Cusp Forms

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

scholarly journals CONSTRUCTING SIMULTANEOUS HECKE EIGENFORMS

2010 ◽  
Vol 06 (05) ◽  
pp. 1117-1137 ◽  
Author(s):  
T. SHEMANSKE ◽  
S. TRENEER ◽  
L. WALLING
Keyword(s):  
Hecke Operators ◽  
Cusp Forms ◽  
Hecke Eigenforms ◽  
Linearly Independent ◽  
Integral Weight ◽  
Trivial Character ◽  
Free Level ◽  
Fixed Space ◽  
Space Of Cusp Forms

It is well known that newforms of integral weight are simultaneous eigenforms for all the Hecke operators, and that the converse is not true. In this paper, we give a characterization of all simultaneous Hecke eigenforms associated to a given newform, and provide several applications. These include determining the number of linearly independent simultaneous eigenforms in a fixed space which correspond to a given newform, and characterizing several situations in which the full space of cusp forms is spanned by a basis consisting of such eigenforms. Part of our results can be seen as a generalization of results of Choie–Kohnen who considered diagonalization of "bad" Hecke operators on spaces with square-free level and trivial character. Of independent interest, but used herein, is a lower bound for the dimension of the space of newforms with arbitrary character.

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