Properties

Label 3024.2.gs
Level 3024
Weight 2
Character orbit gs
Rep. character \(\chi_{3024}(85,\cdot)\)
Character field \(\Q(\zeta_{36})\)
Dimension 5184
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.gs (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 6960 5184 1776
Cusp forms 6864 5184 1680
Eisenstein series 96 0 96

Trace form

\( 5184q + O(q^{10}) \) \( 5184q + 36q^{12} + 84q^{20} + 312q^{50} - 108q^{58} + 72q^{59} + 60q^{60} + 372q^{66} + 156q^{68} + 84q^{72} + 84q^{74} + 168q^{75} + 156q^{78} + 360q^{80} + 60q^{86} - 228q^{92} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database