Weight and level of modular forms
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 ...
11
Modular Forms of Weight One Over Finite Fields
... of modular symbols and a comparison to Hecke algebras of modular ...lar forms will be recalled ...cusp forms over F p , when the weight is between 2 and p − ...As modular ...
111
On Level One Cuspidal Bianchi Modular Forms
... 7) Table 6. the number field generated by the Hecke eigenval- ues of non-lifted newforms in S 0 (1) + We have computed these fields using Dan Yasaki’s program, see [Yas], in Magma which computes the Hecke action on S 0 (Γ ...
17
On vector-valued Siegel modular forms of degree 2 and weight (j,2)
... of level Γ0(2) or Γ0(4), namely the Steinberg representation St and its unramified quadratic twist St ′ in level Γ0(2), and a certain supercuspidal representation Sc in level ...
28
Spaces of modular forms. Modular curves and dimensions
... A year later, Kenneth Ribet proved that this curve is definitely not modular. His strategy consisted in showing that if the Frey curve is associated to a modular form, then it must be associated to one of ...
112
Rankin Eisenstein classes for modular forms
... for modular forms of level prime to p and arbitrary weights; whereas they start from an analogous formula in which the modular forms are taken to have weight 2, but possibly high ...
37
Eigenvarieties associated to Hilbert modular forms
... the weight space the eigenvariety looks like a countable union of ...tame level this was proven by Buzzard-Kilford and Roe in [BK05, ...of modular forms and from this shown that over the ...
137
On Modular Forms and the Inverse Galois Problem
... the level of f and the weight is 2, the field R cannot ramify at ℓ ...Serre weight is 2 and thus that the projective image of inertia I ℓ is cyclic of order ℓ + 1 or ℓ − ...
17
Slopes of Modular Forms and the Ghost Conjecture
... v =v(w − w 62 ) Figure 2. “Halos” centered at k = 62 for the 2-adic ghost series of tame level 1. We have also discovered that the previous result extends to include many more p-adic weights. Specifically, we have ...
18
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 level to each weak function ...with level N |M in the vector space W M ...write modular forms for ...
169
Wach modules and Iwasawa theory for modular forms
... 3.3. Supersingular modular forms. We now apply the theory of Coleman maps developed above to the Galois representations attached to modular forms. Let f = P a n q n be a normalized new ...
46
Dimension Formulae for Spaces of Lifted Bianchi Modular Forms
... 2013 FORMS MEHMET HALUK S ¸ENG ¨ UN AND PANAGIOTIS TSAKNIAS ...base-change forms and their twists inside the space of Bianchi modular forms with fixed (Galois stable) level and ...
7
P adic L functions of Bianchi modular forms
... Bianchi modular symbols Overconvergent modular symbols are modular symbols that take values in a space of p-adic ...Bianchi modular symbols of fixed weight and level, putting us ...
43
A correspondence of modular forms and applications to values of L series
... of modular forms of weight k ≥ 4 is generated by prod- ucts of such Eisenstein series when the level is prime [5], this result implies relations among critical values of L-functions for more ...
12
On the Tamagawa Number Conjecture for motives attached to modular forms
... Note: While every effort has been made to ensure that all stated equalities are exactly true, it is perhaps safer to regard them as holding up to powers of 2 and −1. As we do not consider the TNC at the prime 2, such ...
80
Hilbert modular forms of weight 1/2
... Hilbert modular forms (of half integral weight) are modular forms (of half integral weight) of several ...integral weight modular forms over ...Hilbert ...
45
On Galois representations associated to low weight Hilbert-Siegel modular forms
... In Chapter 5, we prove the first part of Theorem A. Our proof follows a similar struc- ture to the proof of [Ram13, Theorem B]. In Theorem 5.2.1, we prove that, if ρ π,` is reducible, then it decomposes as a direct sum ...
102
VECTOR VALUED SIEGEL MODULAR FORMS OF SYMMETRIC TENSOR WEIGHT OF SMALL DEGREES
... modular forms. We define each ϕ i to be the Eisenstein series of weight i whose constant term is ...of weight 10 or 12 such that the coefficient ...
26
MAASS FORMS, MODULAR FORMS, AND REPRESENTATION THEORY
... by the symbols X and Y , with the standard action of GL(V ) ∼ = GL 2 (C). Consider the symmetric (d − 1)-th power Sym d−1 V = V ⊗(d−1) /hv 1 ⊗ · · · ⊗ v d−1 − v σ(1) ⊗ · · · ⊗ v σ(d−1) i σ∈S d−1 . In this situation, ...
5
Elliptic Modular Forms and Their Applications
... of modular forms of a given weight on Γ is finite dimen- sional and algorithmically computable, so that it is a mechanical procedure to prove any given identity among modular ...Secondly, ...
103