Sym2-Dihedral

This repo contains multiple functions written in PARI/GP about modulars forms, Bernoulli numbers and L-functions. More precisely, on the trace of the symmetric-square L-function and dihedral congruences of modular forms. This code was written as part of my master thesis.

Files

• trace.gp: functions about the trace of the Symmetric square L-function as defined by Dummigan and Heim
• dihedral.gp: functions about dihedral congruences on modular forms
• misc.gp: miscellaneous functions about p-valuation of Bernoulli numbers and modular forms

In a gp session, after reading a file, you can type ? name_of_file to obtain more information about the file.

References

• Ayotte, D, Relations entre le nombre de classes et les formes modulaires, master thesis (2019)
• Dummigan, Neil; Heim, Bernhard, Symmetric square L-values and dihedral congruences for cusp forms. J. Number Theory 130 (2010)
• Brown, Alexander F.; Ghate, Eknath P. Dihedral congruence primes and class fields of real quadratic fields. J. Number Theory 95 (2002)