Properties

Label 3024.2.el
Level 3024
Weight 2
Character orbit el
Rep. character \(\chi_{3024}(107,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 1024
Sturm bound 1152

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3024.el (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 336 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 2352 1024 1328
Cusp forms 2256 1024 1232
Eisenstein series 96 0 96

Trace form

\( 1024q + O(q^{10}) \) \( 1024q + 32q^{16} - 24q^{22} - 12q^{28} + 32q^{34} + 12q^{40} + 12q^{52} + 16q^{58} - 48q^{64} + 64q^{67} - 192q^{70} + 192q^{76} - 20q^{82} + 32q^{88} + 24q^{91} + 60q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database