The Modular Forms Database: Tables

William Stein

My Tables

Modular Abelian Varieties A_f that are Jacobians of Curves

• Basic Data

Hilbert Modular Forms

Elliptic Curves

• Noam Elkies: Tables of Elliptic curves of unit discriminant over real quadratic number fields

Tables Over The Field Q(sqrt(5))

• Dimensions of spaces of Hilbert modular forms, by level
• Factored characteristic polynomials of Hecke operators
• Rational Hilbert modular forms (these correspond to isogeny classes of elliptic curves over Q(sqrt(5)))

Dimensions of Spaces of Cuspforms

• Dimensions of S_k(Gamma₀(N)), S_k(Gamma₁(N)), and S_k(Gamma₁(N))(eps).
• PARI-readable dimension tables for Gamma₀(N)
• MAGMA-readable dimension tables for Gamma₁(N) with character

Characteristic Polynomials

• Characteristic polynomials of T_p on S_k(SL₂(Z))
• Characteristic polynomials of T_p on Gamma₀(N) and Gamma₁(N)
• Discriminants of Hecke algebras
• Arithmetic data about every weight 2 newform on Gamma ₀(N) for all N<5135 (contains charpolys of many eigenvalues).

Eigenvalues and q-expansions of Cuspforms

• q-expansions of newforms
• Basis of cuspforms
• q-expansions of eigenforms on Gamma₀(N) of weight k<=14
• q-expansions of eigenforms on Gamma₁(N) of weight k<=50
• Eigenvalues of modular forms on Gamma₀(N) of weight <=4 and high level, and of weight<=100 and low level
• Eigenforms on Gamma₀(p) in terms of the free-abelian group on supersingular j-invariants

Elliptic Curves

• PARI Tables of Cremona Elliptic Curves
• Isogeny class matrices for elliptic curves of conductor <= 40000
• Lratios L(E,1)/Omega_E for elliptic curves of conductor <= 40000
• Images of Galois Representations
• Cremona's tables of elliptic curves over Q
• Armand Brumer and Oisin McGuinness's table of elliptic curves of prime conductor less than 10⁸ (or try the local mirror)
• The Stein-Watkins database of elliptic curves of conductor up to 10⁸ and of prime conductor up to 10¹⁰.
• Jennifer Sinnott's tables of elliptic curves over number fields
• A systematic table that Cremona made of elliptic curves over quadratic imaginary fields.
• Congruence modulus and modular degree for elliptic curves
• j-invariants of CM elliptic curves
• Pari table of Optimal elliptic curves
• Optimal quotients whose torsion isn't generated by (0)-(oo)

Arithmetic of Newforms, Modular Abelian Varieties, and Modular Curves

• Arithmetic data about every weight 2 newform on Gamma ₀(N) for all N<5135 (and many more up to 7248)
• Component groups of J₀(N)(R) and J₁(N)(R)
• Eigenvalues and invariants for most optimal quotients of J₀(N), N < 3000 for quotients of J₀(N)
• Sha lower bounds (odd parts) for quotients of J₀(N)
• Intersection data (odd parts) for the abelian subvarieties of J₀(N)
• Cuspidal subgroup of J₀(N)
• Order of real component group of J₀(N)
• When is infinity a Weierstrass point on X₀(p)⁺?
• When is infinity a Weierstrass point on X₀(N)?
• Detailed arithmetic data about J_0(11) through J_0(125)
• Modular degree and congruence modulus for N<=500 (except N=183, 292, 317, 341, 476, 487, 488)

Special values of L-functions

• Odd part of the ratio L(A_f,1)/Omega_Af for square-free levels
• Rationals part of the special values of the L-functions of level 1
• Rational part of L(A_f,1) for modular abelian varieties A_f of level up to 1500
• Central critical values for level 1 modular forms of weight <= 200.

p-adic Tables

• Slopes for of charpolys: p=2 and 3 for Gamma₀(N), with N small

Classical Tables

• Antwerp IV (scanned and extended)

Links to Other People's Tables of Modular Forms and Related Data