Package sage :: Package modular :: Package modsym :: Module manin_symbols :: Class ManinSymbolList_gamma0
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Class ManinSymbolList_gamma0

ManinSymbolList --+
                  |
                 ManinSymbolList_gamma0


List of Manin symbols for Gamma0(N).

ManinSymbolList_gamma0(level, weight):
INPUT:
    level -- integer level
    weight -- integer weight >= 2

EXAMPLE:
    >>> m = ManinSymbolList_gamma0(5,2); m
    Manin Symbol List of weight 2 for Gamma0(5)
    >>> m.list()
    [(0, 0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (0, 1, 4)]
    >>> m = ManinSymbolList_gamma0(6,4); m
    Manin Symbol List of weight 4 for Gamma0(6)
    >>> len(m)
    36

Method Summary
  __init__(self, level, weight)
  __repr__(self)
  apply(self, j, m)
Apply the matrix m=[a,b,c,d] to the j-th Manin symbol.
  apply_I(self, j)
  apply_S(self, j)
  apply_T(self, j)
  apply_TT(self, j)
  level(self)
  manin_symbol(self, i)
  normalize(self, x)
    Inherited from ManinSymbolList
  __getitem__(self, n)
  __len__(self)
  index(self, x)
Return the index into the list of Manin symbols of x.
  list(self)
  weight(self)

Method Details

apply(self, j, m)

Apply the matrix m=[a,b,c,d] to the j-th Manin symbol.
INPUT:
    j -- integer
    m = [a, b, c, d] a list of 4 integers.
OUTPUT:
    a list of pairs (j, alpha_i), where each alpha_i is an integer, 
    j is an integer (the j-th sage symbol), and the sum alpha_i*x_i 
    is the image of self under the right action of the matrix [a,b;c,d].
    Here the right action of g=[a,b;c,d] on a Manin symbol [P(X,Y),(u,v)]
    is [P(aX+bY,cX+dY),(u,v)*g].
Overrides:
sage.modular.modsym.manin_symbols.ManinSymbolList.apply

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