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db-MaassWaveForms.md

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Database MaassWaveForms
Description Maass wave forms
Status production
Contact Stefan Lemurell, Fredrik Strömberg
Code modular_forms/maass_forms/maass_waveforms
Collections to be added

Todo: Document or delete the collections below, identify which are actually needed on www.lmfdb.org, and put in links to them in the table above.

Collection Coefficients

  • Field 1: ...
  • Field 2: ...

Collection Coefficients.chunks

  • Field 1: ...
  • Field 2: ...

Collection Coefficients.files

  • Field 1: ...
  • Field 2: ...

Collection DirChars

  • Field 1: ...
  • Field 2: ...

Collection DirCharsConrey

  • Field 1: ...
  • Field 2: ...

Collection DirCharsSage

  • Field 1: ...
  • Field 2: ...

Collection FS

Description: Maassform data.
Field type Example Description
Character integer 1 character number in Conrey numbering if Conrey is set to 1 else in Sage ordering,
Coefficient list [1.0, 1.5493044779412872, 0.24689977245382455, 1.400344365368927] A short list of Fourier coefficients c(1),c(2),...
Conrey integer 1 1 if Conrey character numbers are used, else 0
Contributor string 'HT' identifier of person who originally submitted this data, e.g. 'HT' is Holger Then, FS is Fredrik Stromberg etc. (coefficients may have been added later by other contributors, identified in the corresponding coefficient record)
Cusp_evs list [1] list of (complex) numbers such that the Fourier coefficients at that cusp are proportional to the ones at infinity with this constant. Such constants exists if the corresponding Atkin-Lehner operators are cusp normalisers. The first '1' corresponds to the cusp at infinity.
Dim integer 1 dimension of the eigenspace containing this Maass form (estimated heuristically / numerically)
Dimension integer 1 probably a duplicate of Dim
Eigenvalue float 13.7797513518907 Spectral parameter R corresponding to this Maass form, s.t. the actual eigenvalue is lambda=1/4+R^2
Error float 6.050715484207103e-15 estimate of the error in the eigenvalue}
Level integer 1 level
M0 integer 0 the M0 which was used as input to the algorithm for computing the eigenvalue (if set correctly it should be > 0)
Norm float 1.0 describes the normalisation used for the coefficients, 1.0 means Hecke normalisation so c(1)=1, other} alternatives (not used currently) would be L2-normalisation}
Numc inte 5000 number of coefficients available for this form
Symmetry integer 0 1 if this Maass form is even and 0 if it is odd
Weight float 0.0 the weight of the Maass form
Y float 0 the Y which was used as input to the algorithm for computing the eigenvalue (if set correctly it should be > 0)}
coeff_id objectid ObjectId(4f87f0f388aece21410000e8) id of the corresponding coefficient record
dim integer 1 probably a third duplicate of 'Dim' and 'Dimension'

Collection Table.chunks

  • Field 1: ...
  • Field 2: ...

Collection Table.files

  • Field 1: ...
  • Field 2: ...

Collection metadata

  • Field 1: ...
  • Field 2: ...

Collection maassform_plots

Description: contains plots of Maassforms in the corresponding fundamental domain
  • Field 1: ...
  • Field 2: ...