• LfunctionsAndModularFormsIV
• Discussions
• ModFormHomepage

Discussion for GL(2)

Existing databases

• MODI (Skoruppa) http://modi.countnumber.de/

• The Modular Forms Database (Stein) http://www.wstein.org/Tables/

Home page for space of modular forms

• Dimension.
• Galois information.

• Basis of newforms \left\{f_{1},\ldots,f_{n}\right\}

• Oldspace decomposition

  S_{k}^{old}=\bigoplus_{d,\varepsilon'} S_{k}\left(\Gamma_{0}\left(d\right),\varepsilon'\right)

• Geometric information about X_{0}(N)

• special information?

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

• Fourier coefficients
• Embeddings

• Is f minimal?

  • If not, add minimal guy as a friend.

• Is f CM?

  • If so, add details about the CM.

• Periods (\omega_{\pm})

• Special values (also periods)
• CM-values
• Satake parameters
  • As angles
• Atkin-Lehner eigenvalues
  • Other information about expansions at other cusps
• Closed formulas: general, in terms of e.g. Manin symbols
• Product formulas if available
• "Galois information"
  • In particular for weight 1
  • In general this is still very much only a wish
• Information about liftings from this form.
  • Display some explicit examples.

Friends

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

• Associated minimal form (if f is not minimal)