Package sage :: Package modular :: Package modform :: Module modform :: Class ModularFormElement
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Class ModularFormElement

Known Subclasses:
EisensteinSeries

A modular form.

INPUT:
    parent -- ModularForms (an ambient space of modular forms)
    vector -- a vector on the basis for parent
OUTPUT:
    ModularFormElement -- a modular form
EXAMPLES:
    >>> from sage.modular.congroup import Gamma0
    >>> M = ModularForms(Gamma0(11),2)
    >>> V = M.vector_space()
    >>> f = ModularFormElement(M, V.gen(0))
    >>> f.parent()
    Space of modular forms on Gamma0(11) of weight 2 and dimension 2 over Rational Field

Method Summary
  __init__(self, parent, vector)
  __add__(self, other)
  __cmp__(self, other)
  __getitem__(self, n)
  __getslice__(self, i, j)
  __neg__(self)
  __pos__(self)
  __radd__(self, left)
  __repr__(self)
  __rsub__(self, left)
  __sub__(self, right)
  base_field(self)
  character(self)
  coefficients(self, X)
The coefficients a_n of self, for integers n>=0 in the list X.
  compute(self, X)
Compute the coefficients a_n of self, for integers n>=0 in the list X.
  is_zero(self)
  level(self)
  parent(self)
  prec(self)
  qexp(self, prec)
The q-expansion of the modular form to precision O(q**prec).
  valuation(self)
  weight(self)

Method Details

coefficients(self, X)

The coefficients a_n of self, for integers n>=0 in the list X.

This function caches the results of the compute function.

compute(self, X)

Compute the coefficients a_n of self, for integers n>=0 in the list X. The results need not be cached; use the coefficients method instead for cached results.

qexp(self, prec=None)

The q-expansion of the modular form to precision O(q**prec). This function takes one argument, which is the integer prec.

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