This file was generated on 2023-09-02 by Kilian Bönisch. 


A GENERAL INFORMATION

1. Title of the dataset:
        "Replication Data for: Modularity of special motives of rank four associated with Calabi-Yau threefolds"

2. Brief description of the research project and its aims:
   	This repository contains programs which generate the computational results used in the corresponding doctoral thesis "Modularity of special motives of rank four associated with Calabi-Yau threefolds" (urn:nbn:de:hbz:5-72057). These results are used to compare motives associated with Calabi-Yau threefolds with motives associated with modular forms. The programs perform computations of periods, traces of Frobenius automorphisms and Hecke operators. 

3. Author Information
	Name: Kilian Bönisch
	Institution: Max-Planck-Institut für Mathematik
	Address: Vivatsgasse 7, 53111 Bonn
	Email: kilian@mpim-bonn.mpg.de



B DATA & FILE OVERVIEW

1. File List:
   	The structure of this repositroy is as follows:
       	   - Section5.1/
		- DeformationMethod.gp
		- HeckeEigenvalues.gp
		- PeriodIdentities.gp
		- PointCounting.gp
	   - Section5.2/
		- DeformationMethod.gp
		- HeckeEigenvalues.gp
		- PeriodIdentities.gp
		- PointCounting.gp
	   - Section5.3/
		- DeformationMethod.gp
		- HeckeEigenvalues.mgm
		- PeriodIdentities.gp
		- PointCounting.gp
	   - Section5.4/
		- DeformationMethod.gp
		- HeckeEigenvalues.mgm
		- PeriodIdentities.gp
		- PointCounting.gp
  	   - Section6.3/
	        - ModularityFiberingOut.gp
		- PeriodIdentityLevel1.gp
	   - Section6.4/
		- CohomologyRestrictionInjectivity.mgm
		- FundamentalGroupBases.pdf
		- MonodromyActionFundamentalGroup.gp
	   - Section6.5/
		- HeightIdentities.gp
	The folders correspond to the sections in the related thesis. A brief description of the computations is as follows:
	   - Section5.x:
		- DeformationMethod computes numbers of factorizations of Frobenius polynomials associated with a family of Calabi-Yau threefolds (depending on x).
		- HeckeEigenvalues computes Hecke eigenvalues of (elliptic, Hilbert or Bianchi) modular forms (depending on x).
		- PeriodIdentities numerically computes periods of Calabi-Yau threefolds / modular forms / elliptic curves (depending on x) and compares these.
		- PointCounting computes numbers of points of a Calabi-Yau threefold (depending on x) over finite fields to obtain traces of Frobenius automorphisms.
	   - Section6.3:
		- ModularityFiberingOut computes modular forms associated with pullbacks of hypergeometric functions of rank three.
		- PeriodIdentityLevel1 computes periods of a square root of a modular form of level 1 and compares these with periods of modular form of level 72. 
	   - Section6.4:
		- CohomologyRestrictionInjectivity checks that certain restriction maps from group cohomologies to subgroups are injective.
		- FundamentalGroupBases shows chosen bases of some fundamental groups and actions of monodromy groups on these bases. This data is used in MonodromyActionFundamentalGroup.
		- MonodromyActionFundamentalGroup shows that monodromy actions on some fundamental groups generate sufficiently large spaces.
	   - Section6.5:
		- HeightIdentities computes periods of Calabi-Yau threefolds and compares these with heights (given in terms of derivatives of L-functions). 
	For more details we refer to the description in the related thesis.  

2. Are there multiple versions of the dataset? no



C SHARING/ACCESS INFORMATION

1. Was data derived from another source? no

2. Licenses/restrictions placed on the data:
   	This dataset is available under the Creative Commons CC0 1.0 license: https://creativecommons.org/publicdomain/zero/1.0/

3. Links to publications that cite or use the data: https://nbn-resolving.org/urn:nbn:de:hbz:5-72057 



D METHODOLOGICAL INFORMATION

1. Instrument- and/or software-specific information needed to interpret the data: 
	Scripts ending with ".gp" can be run with PARI/GP (tested with version 2.11.2) and scripts ending with ".mgm" can be run with Magma (tested with version V2.28-2). The results will be printed in the interactive session.