Precalculated Data Storage
Raw Data
Tables of data can be found here:
- Table of primes Hecke operators on modular forms modulo two.
- Table of powers of Hecke operators on modular forms modulo two.
If this is not enough, remember that this module allows anyone to generate new data.
Use of Precalculated Variables
Here is how to use the variables:
- $\ T_p|\Delta^k$ is
Hecke_primes[p][k+1] - $\ T_3^iT_5^j|\Delta^k$ is
Hecke_powers[i+1,j+1][k+1]
These are stored as Δ-series. The q-series of powers of Δ are stored as follows:
- $\ \Delta^k$ is
precalculated[k+1]
Generating Precalculated Data
The various precalculated data generators may be found in the data subfolder. Note that the user may create new data files, if the provided ones aren't enough. Note as well that there are two implemented ways to store data, we advice the binary for speed purposes.
Binary Data Reads
Main.ModularFormsModuloTwo.loadFormListBinary — MethodloadFormListBinary(MAXI, LENGTH)Loads the list of q-coefficients of Δ powers form file.
Main.ModularFormsModuloTwo.loadHeckePowersListBinary — MethodloadHeckePowersListBinary(MAX_POWER, MAX_DELTA)Loads the list of Δ-coefficients of powers of Hecke operators applied to powers of Δ.
Main.ModularFormsModuloTwo.loadHeckePrimesListBinary — MethodloadHeckePrimesListBinary(MAX_PRIME, MAX_DELTA)Loads the list of Δ-coefficients of prime Hecke operators applied to powers of Δ.
Text Data Reads
Main.ModularFormsModuloTwo.loadForm — FunctionloadForm(name, file_name)Load the modular form modulo 2 name from file_name.
Main.ModularFormsModuloTwo.loadFormList — FunctionloadFormList(file_name)Load the modular form list from file_name.
Main.ModularFormsModuloTwo.saveForm — FunctionsaveForm(f, name, file_name)Save the modular form modulo 2 f as name in file_name.
Main.ModularFormsModuloTwo.saveFormList — FunctionsaveFormList(forms_list, file_name)Save the modular forms modulo 2 f as name in file_name.