A space of weight one modular forms attached to totally real cubic number fields

Details A space of weight one modular forms attached to totally real cubic number fields A space of weight one modular forms attached to totally real cubic number fields

2011-09-10

arxiv.org/abs/1109.2251v1

Mathematics

Number Theory

Scientific paper

Let $K$ be a totally real cubic number field with fundamental discriminant. In this note we construct a weight one modular form $f_{K}$ with level and nebentypus depending only on the discriminant of $K$. We show that, up to isomorphism class, the assignment $K \to f_{K}$ is injective. Furthermore, if $d$ is a positive fundamental discriminant we show that $\{f_{K} : K \in \mathcal{C}_{d}\}$ is a linearly independent subset of $\mathcal{M}_{1}(\Gamma_{0}(\mathrm{N}_{d}), \epsilon_{d})$, where $\mathcal{C}_{d}$ denotes the set of isomorphism classes of cubic number fields with discriminant $d$.

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