def _modular_symbols_space_gamma1(self):
"""
Return a space of modular symbols for Gamma1, with level a
random choice from self.levels, weight from self.weights, and
sign chosen randomly from [1, 0, -1].
EXAMPLES:
sage: sage.modular.modsym.tests.Test()._modular_symbols_space_gamma1() # random
level = 3, weight = 4, sign = 0
Modular Symbols space of dimension 2 for Gamma_1(3) of weight 4 with sign 0 and over Rational Field
"""
level, weight, sign = self._level_weight_sign()
M = modsym.ModularSymbols(arithgroup.Gamma1(level), weight, sign)
self.current_space = M
return M
def _modular_symbols_space_character(self):
"""
Return a random space of modular symbols for Gamma1, with
(possibly trivial) character, random sign, and weight a
random choice from self.weights.
EXAMPLES:
sage: sage.modular.modsym.tests.Test()._modular_symbols_space_character() # random
level = 18, weight = 3, sign = 0
Modular Symbols space of dimension 0 and level 18, weight 3, character [1, zeta6 - 1], sign 0, over Cyclotomic Field of order 6 and degree 2
"""
level, weight, sign = self._level_weight_sign()
G = dirichlet.DirichletGroup(level)
eps = G.random_element()
M = modsym.ModularSymbols(eps, weight, sign)
self.current_space = M
return M
