21 views

Skip to first unread message

May 2, 2021, 1:20:52 PM5/2/21

to sage-nt

Dear sage-nt,

Can someone answer this Ask Sage question about

orthonormal eigenbases for spaces of newforms:

Is the requested functionality part of Sage,

perhaps via some external package?

Modularly yours, --Samuel Lelièvre

May 3, 2021, 4:06:54 AM5/3/21

to sage-nt

I will answer it. The solution is to use modular symbols:

sage: N=120

sage: S=ModularSymbols(N,2,+1)

sage: NS=S.new_submodule()

sage: CNS=NS.cuspidal_submodule()

sage: D=CNS.decomposition()

sage: D

[

Modular Symbols subspace of dimension 1 of Modular Symbols space of

dimension 32 for Gamma_0(120) of weight 2 with sign 1 over Rational

Field,

Modular Symbols subspace of dimension 1 of Modular Symbols space of

dimension 32 for Gamma_0(120) of weight 2 with sign 1 over Rational

Field

]

sage: [d.q_eigenform(50) for d in D]

[q + q^3 - q^5 + 4*q^7 + q^9 - 6*q^13 - q^15 - 2*q^17 + 4*q^19 +

4*q^21 - 8*q^23 + q^25 + q^27 - 6*q^29 - 4*q^35 - 6*q^37 - 6*q^39 +

10*q^41 - 4*q^43 - q^45 + 8*q^47 + 9*q^49 + O(q^50),

q + q^3 + q^5 + q^9 - 4*q^11 + 6*q^13 + q^15 - 6*q^17 - 4*q^19 + q^25

+ q^27 - 2*q^29 - 8*q^31 - 4*q^33 - 2*q^37 + 6*q^39 - 6*q^41 + 12*q^43

+ q^45 + 8*q^47 - 7*q^49 + O(q^50)]

> --

> You received this message because you are subscribed to the Google Groups "sage-nt" group.

> To unsubscribe from this group and stop receiving emails from it, send an email to sage-nt+u...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/68cb967b-aded-42e3-b14a-436eeba8268dn%40googlegroups.com.

sage: N=120

sage: S=ModularSymbols(N,2,+1)

sage: NS=S.new_submodule()

sage: CNS=NS.cuspidal_submodule()

sage: D=CNS.decomposition()

sage: D

[

Modular Symbols subspace of dimension 1 of Modular Symbols space of

dimension 32 for Gamma_0(120) of weight 2 with sign 1 over Rational

Field,

Modular Symbols subspace of dimension 1 of Modular Symbols space of

dimension 32 for Gamma_0(120) of weight 2 with sign 1 over Rational

Field

]

sage: [d.q_eigenform(50) for d in D]

[q + q^3 - q^5 + 4*q^7 + q^9 - 6*q^13 - q^15 - 2*q^17 + 4*q^19 +

4*q^21 - 8*q^23 + q^25 + q^27 - 6*q^29 - 4*q^35 - 6*q^37 - 6*q^39 +

10*q^41 - 4*q^43 - q^45 + 8*q^47 + 9*q^49 + O(q^50),

q + q^3 + q^5 + q^9 - 4*q^11 + 6*q^13 + q^15 - 6*q^17 - 4*q^19 + q^25

+ q^27 - 2*q^29 - 8*q^31 - 4*q^33 - 2*q^37 + 6*q^39 - 6*q^41 + 12*q^43

+ q^45 + 8*q^47 - 7*q^49 + O(q^50)]

> You received this message because you are subscribed to the Google Groups "sage-nt" group.

> To unsubscribe from this group and stop receiving emails from it, send an email to sage-nt+u...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/68cb967b-aded-42e3-b14a-436eeba8268dn%40googlegroups.com.

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu