Properties

Label 3024.2.fz
Level 3024
Weight 2
Character orbit fz
Rep. character \(\chi_{3024}(239,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 648
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.fz (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 3528 648 2880
Cusp forms 3384 648 2736
Eisenstein series 144 0 144

Trace form

\( 648q + O(q^{10}) \) \( 648q - 36q^{33} - 36q^{41} + 36q^{57} + 72q^{65} + 72q^{81} + 108q^{89} + 144q^{93} - 108q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database