Revision history [back]
 | 1 | initial version |
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 + 4q^7 + q^9 - 6q^13 - q^15 - 2q^17 + 4q^19 + 4q^21 - 8q^23 + q^25 + q^27 - 6q^29 - 4q^35 - 6q^37 - 6q^39 + 10q^41 - 4q^43 - q^45 + 8q^47 + 9q^49 + O(q^50), q + q^3 + q^5 + q^9 - 4q^11 + 6q^13 + q^15 - 6q^17 - 4q^19 + q^25 + q^27 - 2q^29 - 8q^31 - 4q^33 - 2q^37 + 6q^39 - 6q^41 + 12q^43 + q^45 + 8q^47 - 7*q^49 + O(q^50)]
| | 2 | No.2 Revision |
The solution is to use modular symbols:
sage: `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 + 4q^7 + q^9 - 6q^13 - q^15 - 2q^17 + 4q^19 + 4q^21 - 8q^23 + q^25 + q^27 - 6q^29 - 4q^35 - 6q^37 - 6q^39 + 10q^41 - 4q^43 - q^45 + 8q^47 + 9q^49 + O(q^50),
q + q^3 + q^5 + q^9 - 4q^11 + 6q^13 + q^15 - 6q^17 - 4q^19 + q^25 + q^27 - 2q^29 - 8q^31 - 4q^33 - 2q^37 + 6q^39 - 6q^41 + 12q^43 + q^45 + 8q^47 - 7*q^49 + O(q^50)]
| | 3 | No.3 Revision |
The solution is to use modular symbols:
`sage:
sage: | | 4 | No.4 Revision |
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)]
Sorry about bad formatting.
You can also see this space (weight 2, level 120, trivial character) on the LMFDB at http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/?level=120&weight=2&char_order=1&search_type=List and then go to each newform's home page, e.g. http://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/120/2/a/a/
