was@form:~$ sage -------------------------------------------------------------- ----- | SAGE Version 0.9.12, Build Date: 2005-11-22-0059 | | Distributed under the terms of the GNU General Public Licen se | | For help type ?, ??, %magic, or help | -------------------------------------------------------------- ----- sage: dimension_modular_forms(Gamma1(5000),2) _1 = 756600 sage: dimension_modular_forms(Gamma0(5000),2) _2 = 810 sage: G = DirichletGroup(5) sage: G _4 = Group of Dirichlet characters of modulus 5 over Cyclotom ic Field of order 4 and degree 2 sage: list(G) _5 = [[1], [zeta_4], [-1], [-zeta_4]] sage: sage: eps = G.0 sage: eps _7 = [zeta_4] sage: eps(2) _8 = zeta_4 sage: eps(932840923840982) _9 = zeta_4 sage: eps(93284092384098939121)