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Let $d$ be a positive fundamental discriminant, and let $\mathcal{C}_{d}$ bethe set of isomorphism classes of cubic number fields of discriminant $d$. Foreach $K \in \mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ withlevel $3^{\pm 1}d$ and nebentypus $\left( \frac{-3^{\pm 1}d}{\cdot} \right)$.We show that the form $f_{K}$ completely determines the field $K$. Moreover, weshow that $\{f_{K} : K \in \mathcal{C}_{d}\}$ is a linearly independent set.

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