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

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

2007-07-16

arxiv.org/abs/0707.2365v1

Mathematics

Number Theory

Scientific paper

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 $E$.

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