Let be a totally real number field of degree . Let be the real embeddings of , and for abbreviate and extend this elementwise to matrices. Write if is totally positive and .
Let be positive integers of the same parity, and let be a nonzero ideal of the ring of integers of .
For an ideal , let
A Hilbert modular form of weight and level is a tuple of holomorphic functions , indexed by ideals representing the narrow class group of , such that for all and all we have
A Hilbert cusp form is a Hilbert modular form that vanishes at the cusps.
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- Review status: beta
- Last edited by John Voight on 2024-06-18 08:40:06
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- ec.curve_label
- mf
- mf.hilbert.hecke_orbit
- mf.hilbert.label
- mf.hilbert.search_input
- mf.hilbert.weight_vector
- rcs.cande.lfunction
- rcs.rigor.lfunction.modular
- rcs.source.ec
- rcs.source.lfunction.modular
- lmfdb/hilbert_modular_forms/hilbert_modular_form.py (line 63)
- lmfdb/hilbert_modular_forms/hmf_stats.py (line 42)
- lmfdb/hilbert_modular_forms/hmf_stats.py (line 49)
- lmfdb/lfunctions/Lfunction.py (line 988)
- 2024-06-18 08:40:06 by John Voight
- 2024-06-18 08:39:23 by John Voight
- 2024-05-14 21:05:09 by John Voight
- 2019-04-30 23:35:23 by John Voight
- 2019-04-26 19:05:46 by Holly Swisher
- 2013-03-20 10:17:02 by Lassina Dembele