42.7 Modular Forms over a Non-minimal Base Ring

Module: sage.modular.modform.ambient_R

Modular Forms over a Non-minimal Base Ring

Class: ModularFormsAmbient_R

class ModularFormsAmbient_R
ModularFormsAmbient_R( self, M, base_ring)

Ambient space of modular forms over a ring other than QQ.

sage: M = ModularForms(23,2,base_ring=GF(7)) ## indirect doctest
sage: M
Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of
weight 2 over Finite Field of size 7
sage: M == loads(dumps(M))
True

Special Functions: __init__,$ \,$ _compute_q_expansion_basis,$ \,$ _repr_

_compute_q_expansion_basis( self, [prec=None])

Compute q-expansions for a basis of self to precision prec.

sage: M = ModularForms(23,2,base_ring=GF(7))        
sage: M._compute_q_expansion_basis(5)
[1 + 5*q^3 + 5*q^4 + O(q^5),
q + 6*q^3 + 6*q^4 + O(q^5),
q^2 + 5*q^3 + 6*q^4 + O(q^5)]

_repr_( self)

String representation for self.

sage: M = ModularForms(23,2,base_ring=GF(7)) ## indirect doctest
sage: M._repr_()
'Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of
weight 2 over Finite Field of size 7'

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