Weights of modular forms on $\mathrm{SO}^{+}(2,l)$ and congruences between Eisenstein series and cusp forms of half-integral weight on $\mathrm{SL}_{2}$

Richard Hill

Weights of modular forms on $\mathrm{SO}^{+}(2,l)$ and congruences between Eisenstein series and cusp forms of half-integral weight on $\mathrm{SL}_{2}$

Number Theory 2007-07-17 v1

Authors: Richard Hill

Abstract

Let $E$ be a level 1, vector valued Eisenstein series of half-integral weight, normalized so that the coefficients are all in $\mathbb{Z}$ . We show that there is a level one vector valued cusp form $f$ with the same weight as $E$ and with coefficients in $\mathbb{Z}$ , which is congruent to $E$ modulo the constant term of $E$ .

Keywords

modular forms Eisenstein series cusp forms half-integral weight congruences vector valued forms SL2 SO+(2,l)

Cite

@article{arxiv.0707.2365,
  title  = {Weights of modular forms on $\mathrm{SO}^{+}(2,l)$ and congruences between Eisenstein series and cusp forms of half-integral weight on $\mathrm{SL}_{2}$},
  author = {Richard Hill},
  journal= {arXiv preprint arXiv:0707.2365},
  year   = {2007}
}

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