## Abstract

Let Alev A_{11}^{lev} be the moduli space of (1, 11)-polarized abelian surfaces with a canonical level structure. Let χ be a primitive character of order 5 with conductor 11. In this paper we construct five endoscopic lifts Π_{i}, 0≤i≤4 from two elliptic modular forms f ⊗χi of weight 2 and g⊗X^{i} of weight 4 with complex multiplication by Q(√ -11) such that Πi∞ gives a non-holomorphic differential form on Alev A_{11}^{lev} for each i, 0 ≤ i ≤ 4. Then their spinor L-functions are of form L(s-1,f ⊗χi)L(s,g⊗χi) such that L(s,g⊗χi) does not appear in the L-function of Alev A_{11}^{lev} for any i, 0 ≤ i ≤ 4. The existence of such lifts is motivated by the computation of the L-function of Klein's cubic threefold which is a birational smooth model of Alev A_{11}^{lev}.

Original language | English |
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Pages (from-to) | 183-205 |

Number of pages | 23 |

Journal | American Journal of Mathematics |

Volume | 135 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Feb |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)