Properties

Label 3024.2.en
Level 3024
Weight 2
Character orbit en
Rep. character \(\chi_{3024}(19,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 752
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.en (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1008 \)
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 784 1568
Cusp forms 2256 752 1504
Eisenstein series 96 32 64

Trace form

\( 752q - 2q^{2} + 2q^{4} - 4q^{7} + 16q^{8} + O(q^{10}) \) \( 752q - 2q^{2} + 2q^{4} - 4q^{7} + 16q^{8} - 12q^{10} + 4q^{11} - 6q^{14} + 2q^{16} + 24q^{17} - 12q^{19} - 4q^{22} + 8q^{23} + 12q^{26} - 16q^{28} + 4q^{29} + 18q^{32} + 12q^{34} - 2q^{35} - 4q^{37} - 4q^{43} + 26q^{44} - 12q^{46} - 4q^{49} - 4q^{50} + 4q^{53} + 96q^{56} - 4q^{58} + 6q^{59} - 6q^{61} - 16q^{64} - 4q^{65} + 2q^{67} + 12q^{70} + 32q^{71} - 52q^{74} + 58q^{77} + 12q^{80} + 60q^{83} - 14q^{85} + 44q^{86} - 4q^{88} - 36q^{91} + 20q^{92} - 6q^{94} - 22q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database