Steinberg Homology, Modular Forms, and Real Quadratic Fields

\(\Gamma = \Gamma_0(N)^{\pm} \leq \mathrm{GL}_2(\mathbb{Z})\) Data

• with-torsion-eldiv.txt:
  Each data line has the form N:cuspdim,tor:eldiv:t_def:d_list,
  where N is the level, cuspdim is the free rank and tor is torsion of \(H_0^{\text{cusp}}(\Gamma,\mathrm{St}(\mathbb{Q}^2))\), t_def is a supplemental bit of information, eldiv is the list of elementary divisors of the image of \(\psi_{\Gamma, E}\), and d_list is the list of squarefree \(\Delta\) for \(E = \mathbb{Q}(\sqrt{\Delta})\) that have this data.
• ane-summary.txt:
  Each data line has the form N,U,A,Q,num_roots,ane_list,
  where N is the level, U, A, Q are defined in Section 15 of the paper, num_roots is a supplemental bit of information, and ane_list is the list of squarefree \(\Delta\) for \(E = \mathbb{Q}(\sqrt{\Delta})\) that have this data.

\(\Gamma = \Gamma_0(N) \leq \mathrm{SL}_2(\mathbb{Z})\) Data

• SL-with-torsion-eldiv.txt
  Each data line has the form N:cuspdim,tor:eldiv:t_def:d_list,
  where N is the level, cuspdim is the free rank and tor is torsion of \(H_0^{\text{cusp}}(\Gamma,\mathrm{St}(\mathbb{Q}^2))\), t_def is a supplemental bit of information, eldiv is the list of elementary divisors of the image of \(\psi_{\Gamma, E}\), and d_list is the list of squarefree \(\Delta\) for \(E = \mathbb{Q}(\sqrt{\Delta})\) that have this data.
• SL-ane-summary.txt:
  Each data line has the form N,U,A,Q,num_roots,ane_list,
  where N is the level, U, A, Q are defined in Section 15 of the paper, num_roots is a supplemental bit of information, and ane_list is the list of squarefree \(\Delta\) for \(E = \mathbb{Q}(\sqrt{\Delta})\) that have this data.