Database siegel_modular_forms


Description	Siegel modular forms
Status	production
Contact	Nils Skouruppa, Andrew Sutherland
Code	siegel_modular_forms
Collections	dimensions, samples, families
Todo: Add details expanding on utilitarian descriptions below

Collection samples

_id: ObjectId assigned by mongo db (referenced by owner_id below, must not change when moving/copying)
data_type: string equal to one of "sample", "ev", or "fc"

Records with data_type equal to "sample" contain the following additional fields:

collection: array of strings identifying families of spaces of Siegel modular forms that contain this sample (the families currently defined are not disjoint, so the same sample may appear in multiple families)
name: name uniquely identifying the sample within any of the collections it belongs to
courtesy_of: string identifying the source of the sample (e.g. authors and date)
deg: integer degree of the form (forms on M_k(Sp(2d)) have degree d, currently we have samples for d=2,3,4)
fdeg: integer degree of field_poly (current an integer in [1..29])
field_poly: string encoding a monic polynomial f(x) in Z[x] defining a number field Q(a):=Q[x]/(f(x)) (x is used for Q)
explicit_formula: string encoding a polynomial in Q(a)[A,B,C,D]
is_eigenform: boolean
is_integral: boolean
representation: string encoding an integer (currently an element of {0,2})
data_type: string describing the type of sample (e.g. "Ikeda lift, cusp form")
wt: integer weight (currently an even integer in [2,58])

Records with data_type equal to "ev" (eigenvalue) contain the following additional fields:

owner_id: Object(id) equal to the _id attribute of the sample to which this eigenvalue data belongs
index: string encoding the integer index of the eigenvalue (currently an integer in [2..100]). This uniquely identifies the eigenvalue among other eigenvalues with the same owner_id.
data: string encoding the eigenvalue as an element of the number field Q(a) of the sample (as defined by field_poly)

Records with data_type equal to "fc" (Fourier coefficient) contain the following additional fields:

owner_id: Object(id) equal to the _id attribute of the sample to which this Fourier coefficient data belongs
det: string encoding an integer that uniquely identifies this Fourier coefficient data record among others with the same owner_id (currently an integer in [0..2999])
data: dictionary whose keys are strings encoding integer vectors and whose values are strings encoding (possibly constant) polynomials in Q(a)[x,y]

_id: ObjectId assigned by mongo db
title: string (currently always set to "Hilbert Poincare series")
group: name of the modular group, string (currently always "Gamma(2)")
description: string describing the space
space: string describing the type of the space (either "total" or "cusp")
sym_power: string encoding a nonnegative even integer (currently in [0,100])
note: string containing a latex note
author: string naming the author(s)
111111: string encoding a rational function in Q(t)
21111: string encoding a rational function in Q(t)
2211: string encoding a rational function in Q(t)
222: string encoding a rational function in Q(t)
3111: string encoding a rational function in Q(t)
321: string encoding a rational function in Q(t)
33: string encoding a rational function in Q(t)
411: string encoding a rational function in Q(t)
42: string encoding a rational function in Q(t)
51: string encoding a rational function in Q(t)
6: string encoding a rational function in Q(t)

_id: ObjectedId assigned by mongo db
name: string identifying the family (e.g. "Sp4Z")
*degree: integer degree of the famly (currently 2, 3, or 4)
latex_name: latex string for displaying the name
order: integer used to control the ordering of the families for display purposes
dim_args_default: for families with dimension formulas, a dictionary with default values for k and j