• LfunctionsAndModularFormsIV
• Discussions
• HilbModFormHomepage

Discussion for Hilbert modular forms

Existing databases

• Unpublished work of Dembele
• Unpublished work of Donnelly and Voight

Home page for Hilbert modular forms over a totally real field

• Field data
  • coefficients of minimal polynomial
  • basis for ring of integers
  • basis for unit group
  • class number, strict class number
  • class numbers of cyclotomic quadratic extensions
  • ...
• Primitives for definite or indefinite method
  • Quaternion algebra of discriminant 1
  • maximal order
  • (strict) ideal classes
    • corresponding theta series
  • Fuchsian group generators
    • fundamental domain
• Weights and levels of known spaces

Home page for a space of Hilbert modular forms

• Field
• Level
• Weight
• Character
• Dimension
  • local embedding numbers
• Galois information
• Constituent forms
• Oldspace decomposition

• \mathbb Z-module of integral q-expansions (for congruences and for pairings)

Home page for (the Galois orbit of) a modular form f

• Field, level, weight, character
• Hecke eigenvalues
• Hecke polynomial
  • As small linear combination of Hecke operators
• Fourier coefficients
• Embeddings

• Is f minimal?

  • If not, add minimal guy as a friend.

• Is f CM?

  • If so, add details about the CM.

• Is f a base change?

  • If so, give a link to the base changed form (e.g. over \mathbb Q)

• Periods (\omega_{\pm})

• Special values (also periods)
• CM-values
• Satake parameters
  • As angles
• Atkin-Lehner eigenvalues
• Closed formulas?
• Field for easy exporting into Sage, Magma, ...

Friends

• Associated L-function
• Associated elliptic (or other) curve

• Associated minimal form (if f is not minimal)