7.2.1.2 ModularFormElement Objects

class ModularFormElement
An element of a space of modular forms.
ModularFormElement( parent, vector)

INPUT:
    parent -- ModularForms (an ambient space of modular forms)
    vector -- a vector on the basis for parent
OUTPUT:
    ModularFormElement -- a modular form

sage: from sage.modular.congroup import Gamma0
sage: M = ModularForms(Gamma0(11),2)
sage: V = M.vector_space()
sage: f = ModularFormElement(M, V.gen(0))
sage: f.parent()
Space of modular forms on Gamma0(11) of weight 2 and dimension
2 over Rational Field

Instances of class ModularFormElement have the following methods (in addition to inherited methods and special methods):

base_field,$  $ character,$  $ coefficients,$  $ compute,$  $ is_zero,$  $ level,$  $ parent,$  $ prec,$  $ qexp,$  $ valuation,$  $ weight

These methods are defined as follows:

base_field( )

character( )

coefficients( 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( 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.

is_zero( )

level( )

parent( )

prec( )

qexp( [prec=None])

The $ q$ -expansion of the modular form to precision $ O(q^{\rm prec})$ . This function takes one argument, which is the integer prec.

valuation( )

weight( )

Instances of class ModularFormElement also have the following special methods:

__add__( other)

__cmp__( other)

__getitem__( n)

__getslice__( i, j)

__neg__( )

__pos__( )

__radd__( left)

__rsub__( left)

__sub__( right)

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