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 Newforms of level $4$ and of trivial character Commun. Korean Math. Soc. 2014 Vol. 29, No. 4, 497-503 https://doi.org/10.4134/CKMS.2014.29.4.497Printed October 1, 2014 Yichao Zhang University of Connecticut Abstract : In this paper, we consider characters of $\text{SL}_2(\mathbb Z)$ and then apply them to newforms of integral weight, level $4$ and of trivial character. More precisely, we prove that all of them are actually level $1$ forms of some nontrivial character. As a byproduct, we prove that they all are eigenfunctions of the Fricke involution with eigenvalue $-1$. Keywords : Fricke involution, non-Dirichlet character MSC numbers : Primary 11F11, 11F06 Downloads: Full-text PDF

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