## Abstract

We prove that a Dirichlet series with a functional equation and Euler product of a particular form can only arise from a holomorphic cusp form on the Hecke congruence group Gamma(0)(13). The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredient is a generalization of the familiar Weil's lemma that played a prominent role in previous converse theorems.

Translated title of the contribution | A converse theorem for Gamma (0) (13) |
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Original language | English |

Pages (from-to) | 314 - 323 |

Number of pages | 10 |

Journal | Journal of Number Theory |

Volume | 122 (2) |

Publication status | Published - Feb 2007 |