A trace formula for hecke operators on L2(S2) and modular forms on Γ0(4)

2001 ◽  
Vol 71 (1) ◽  
pp. 181-196
Author(s):  
J. Elstrodt
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Hecke Operators

A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS

2016 ◽  
Vol 59 (1) ◽  
pp. 143-165
Author(s):  
NICOLE RAULF ◽  
OLIVER STEIN
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Hecke Operators ◽  
Weil Representation ◽  
Cusp Forms ◽  
Dimension Formula ◽  
Integral Weight ◽  
Vector Valued

AbstractWe present a ready to compute trace formula for Hecke operators on vector-valued modular forms of integral weight for SL2(ℤ) transforming under the Weil representation. As a corollary, we obtain a ready to compute dimension formula for the corresponding space of vector-valued cusp forms, which is more general than the dimension formulae previously published in the vector-valued setting.

scholarly journals An elementary proof of the Eichler–Selberg trace formula

2020 ◽  
Vol 2020 (762) ◽  
pp. 105-122 ◽  
Author(s):  
Alexandru A. Popa ◽  
Don Zagier
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Modular Group ◽  
Algebraic Property ◽  
Double Coset ◽  
Kernel Functions ◽  
Hecke Operators ◽  
Congruence Subgroups ◽  
The Right ◽  
Number Relation

AbstractWe give a purely algebraic proof of the trace formula for Hecke operators on modular forms for the full modular group{\mathrm{SL}_{2}(\mathbb{Z})}, using the action of Hecke operators on the space of period polynomials. This approach, which can also be applied for congruence subgroups, is more elementary than the classical ones using kernel functions, and avoids the analytic difficulties inherent in the latter (especially in weight two). Our main result is an algebraic property of a special Hecke element that involves neither period polynomials nor modular forms, yet immediately implies both the trace formula and the classical Kronecker–Hurwitz class number relation. This key property can be seen as providing a bridge between the conjugacy classes and the right cosets contained in a given double coset of the modular group.

scholarly journals A trace formula for vector-valued modular forms

2015 ◽  
Vol 17 (06) ◽  
pp. 1550069
Author(s):  
P. Bantay
Keyword(s):  
Trace Formula ◽  
Modular Forms ◽  
Weight Distribution ◽  
Hilbert Polynomial ◽  
Free Generators ◽  
Vector Valued

We present a formula for vector-valued modular forms, expressing the value of the Hilbert-polynomial of the module of holomorphic forms evaluated at specific arguments in terms of traces of representation matrices, restricting the weight distribution of the free generators.

scholarly journals Hecke’s modular forms by functional equations

2018 ◽  
Vol 14 (05) ◽  
pp. 1247-1256
Author(s):  
Bernhard Heim
Keyword(s):  
Modular Forms ◽  
Functional Equations ◽  
Hecke Operators ◽  
General Context ◽  
Periodic Functions

We investigate the interplay between multiplicative Hecke operators, including bad primes, and the characterization of modular forms studied by Hecke. The operators are applied on periodic functions, which lead to functional equations characterizing certain eta-quotients. This can be considered as a prototype for functional equations in the more general context of Borcherds products.

scholarly journals Hecke operators on differential modular forms mod p

2012 ◽  
Vol 132 (5) ◽  
pp. 966-997 ◽  
Author(s):  
Alexandru Buium ◽  
Arnab Saha
Keyword(s):  
Modular Forms ◽  
Hecke Operators ◽  
Differential Modular Forms ◽  
Mod P

scholarly journals Construction of siegel modular forms of degree three and commutation relations of Hecke operators

1985 ◽  
Vol 100 ◽  
pp. 83-96 ◽  
Author(s):  
Yoshio Tanigawa
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Siegel Modular Forms ◽  
Hecke Operators ◽  
Weil Representation ◽  
Commutation Relations ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Shimura Correspondence

In connection with the Shimura correspondence, Shintani [6] and Niwa [4] constructed a modular form by the integral with the theta kernel arising from the Weil representation. They treated the group Sp(1) × O(2, 1). Using the special isomorphism of O(2, 1) onto SL(2), Shintani constructed a modular form of half-integral weight from that of integral weight. We can write symbolically his case as “O(2, 1)→ Sp(1)” Then Niwa’s case is “Sp(l)→ O(2, 1)”, that is from the halfintegral to the integral. Their methods are generalized by many authors. In particular, Niwa’s are fully extended by Rallis-Schiffmann to “Sp(l)→O(p, q)”.

Sign in / Sign up

Export Citation Format

Share Document