Properties

Label 3024.2.er
Level 3024
Weight 2
Character orbit er
Rep. character \(\chi_{3024}(253,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 576
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.er (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 144 \)
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 576 1776
Cusp forms 2256 576 1680
Eisenstein series 96 0 96

Trace form

\( 576q + O(q^{10}) \) \( 576q + 28q^{20} - 64q^{26} + 56q^{38} - 48q^{46} + 288q^{49} - 52q^{50} + 36q^{58} + 24q^{59} + 24q^{62} + 72q^{64} + 52q^{68} + 28q^{74} - 24q^{76} + 304q^{80} + 72q^{82} + 124q^{86} + 48q^{88} - 76q^{92} + 128q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database