Modular Forms are Determined by Coefficients Modulo n
Spaces of modular forms. Modular curves and dimensions
... Complex elliptic curves The compact Riemann surfaces of genus equal to 1 are called complex elliptic curves for reasons to be explained in this chapter. It is possible to prove that any complex elliptic curve is ...
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MAASS FORMS, MODULAR FORMS, AND REPRESENTATION THEORY
... and similarly for L, H, and all elements of K. So, as claimed, nothing except the scalar by which Z acts is changed (in particular the action of ∆ is determined by that of H, R, L). Also, by looking at the ...
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Contributions to the theory of modular forms and L-functions
... cusp forms of weight 2 ≤ k ≤ 14, k 6= 12, for the full modular ...integer N such that ω( N z ) only has poles in ...level N |M in the vector space W M ...write modular ...
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Wach modules and Iwasawa theory for modular forms
... to modular forms. Let f = P a n q n be a normalized new eigenform of weight k and character ...(a n : n ≥ 1), which is the completion of the coefficient field F of f at the prime ...
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Theta lifts of Bianchi modular forms and applications to paramodularity
... Remark 5.4. The index entries in Table 1 are based on finite sets of Hecke eigenvalues. Since there is no analogue of Sturm’s bound for Bianchi modular forms, the last row entries are not proved to be ...
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Modular Forms of Weight One Over Finite Fields
... As modular forms in the situation when we consider them are uniquely determined by their q-expansions, we only need to compute the corresponding Hecke algebra, since the space of modular ...
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Cuspidality and the growth of Fourier coefficients of modular forms: A survey
... ≥ n/2. When k < n/2, all modular forms are singular, ...Fourier coefficients are supported only over degenerate indices, so that they can not be cuspidal, unless ...cusp forms ...
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A p-adic property of Fourier coefficients of modular forms of half integral weight. P. Guerzhoy
... The lllodular forms which appears in the left hand side of (4), are linear combinations of theta series. We apply our proposition 1 to these theta series. The proposition asserts that fo[r] ...
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Borcherds found a remarkable multiplicative correspondence between classical modular forms with poles at cusps and meromorphic modular forms on complex varieties SO(n
... log |1 − exp (2πi(˜λ + , v)| . Notice that all terms here except c(0) log (ǫ) are locally sums of holomorphic and anti-holomorphic functions of v. Let us now assume that the coefficients c(n) of F are ...
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EXPLICIT METHODS FOR HILBERT MODULAR FORMS
... If N - 61, then dim S 2 (N) new ≤ 2: each newform f of conductor N has rational Fourier coefficients and is either the base change of a classical modular form over Q or associated to an ...
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CiteSeerX — On signs of Fourier coefficients of cusp forms
... Fourier coefficients of classical modular forms, or equivalently Hecke eigenvalues: first, we give an upper bound for the size of the first sign-change of Hecke eigenvalues in terms of conductor and ...
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UNIMODAL SEQUENCES AND QUANTUM AND MOCK MODULAR FORMS
... twists modulo Q, one obtains a weight 1/2 weakly holomorphic modular ...holomorphic forms of half-integer weight which are congruent to cusp forms modulo ...cusp forms, which by ...
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Images of adelic Galois representations for modular forms
... Remark 2.1.2. Our normalizations are such that if f has weight 2, ρ f,p is the representation appearing in the ´ etale cohomology of X 1 (N) with trivial coefficients. Some authors use an alternative ...
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Weight Reduction for Mod l Bianchi Modular Forms
... As an immediate corollary of the above, we get Corollary 1.2. Mod ℓ, there are only finitely many eigenvalue systems with fixed level. Note that due to the possible existence of torsion in the second cohomology with ...
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On congruences of modular forms over imaginary quadratic fields
... matrix N ∗ degenerates modulo l, and by “sc” we mean that the conductor of a supercuspidal representation of GL(2, Q p ) degenerates modulo l; note that by Remark ...trivial modulo l, and ...
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Euler systems for Rankin Selberg convolutions of modular forms
... As remarked above, g m is an eigenform for the Hecke operators away from mN ; so we may now apply exactly the same formal manipulations as in the proof of [Kat04, Proposition 7.1], but with group ring coefficients ...
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Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square
... Cite this article as: Hakami: Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square.[r] ...
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Estimates for lattice points of quadratic forms with integral coefficients modulo a prime number square (II)
... n– log n p . The error term p n in the upper bound ... n– log n p in the asymptotic estimate at the expense of having to place a constant larger than on the main ...p n ...
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the Coefficients in the Expansions of Certain Modular Functions.
... generating modular function / (q)or cf> ( t ) satisfies an equation * ( T ) - ( « + * r ) p + ( i ± * : ), ...The coefficients in their expansions are integral, but possess otherwise no particular ...
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Permutation Polynomials modulo $p^n$}
... Polynomials modulo p n Rajesh P Singh ∗ Soumen Maity † Abstract A polynomial f over a finite ring R is called a permutation polynomial if the mapping R → R defined by f is ...the coefficients of a ...
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