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Properties

Label 3024.2.en
Level $3024$
Weight $2$
Character orbit 3024.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

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

Display 100 coefficients 10 coefficients

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

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