We prove Ibukiyama’s conjectures on Siegel modular forms of half-integral weight and degree 2 by using Arthur’s multiplicity formula the split odd special orthogonal group $${\text {SO}}_5$$ Gan–Ichino’s metaplectic {Mp}}_4$$ . In proof, representation theory Jacobi groups also plays an important role.

We explicitly solve a collection of binomial Thue equations with unknown degree and unknown S-unit coefficients, for a number of sets S of small cardinality. Equivalently, we characterize integers x such that the polynomial x2 + x assumes perfect power values, modulo S-units. These results are proved through a combination of techniques, including Frey curves and associated modular forms, lower ...

In this paper we consider level stripping for genus 2 cuspidal Siegel eigenforms. In particular, we show that it is possible to strip primes from the level of Saito-Kurokawa lifts that arise as theta lifts and weak endoscopic lifts with a mild condition on the associated character. The main ingredients into our results are a level stripping result for elliptic modular forms and the explicit nat...

The aim of this paper is to give the dimension of the space of Siegel modular forms M k (Γ(3)) of degree 2, level 3 and weight k for each k. Our main result is Theorem dim M k (Γ(3)) = 1 2 (6k 3 − 27k 2 + 79k − 78) k ≥ 4. In other words we have the generating function : ∞ k=0 dim M k (Γ(3))t k = 1 + t + t 2 + 6t 3 + 6t 4 + t 5 + t 6 + t 7 (1 − t) 4. About the space of cusp forms, the dimension ...

is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg [13] for even n and by Pfetzer [9] for odd n. Shimura [14] generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta s...