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Properties

Label 3024.2.gq
Level $3024$
Weight $2$
Character orbit 3024.gq
Rep. character $\chi_{3024}(205,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $6864$
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.gq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3024 \)
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 6960 0
Cusp forms 6864 6864 0
Eisenstein series 96 96 0

Trace form

\( 6864 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 24 q^{6} - 12 q^{8} + O(q^{10}) \) \( 6864 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 24 q^{6} - 12 q^{8} + 6 q^{10} - 6 q^{11} - 6 q^{12} - 24 q^{13} - 12 q^{14} - 48 q^{15} - 6 q^{16} + 12 q^{17} - 6 q^{18} + 6 q^{19} - 24 q^{20} - 12 q^{21} - 24 q^{22} - 126 q^{24} - 12 q^{26} - 24 q^{27} - 24 q^{28} - 24 q^{29} - 6 q^{30} - 12 q^{31} - 6 q^{32} - 12 q^{33} - 36 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 6 q^{38} - 6 q^{40} + 18 q^{42} - 24 q^{43} - 12 q^{44} - 6 q^{45} - 12 q^{46} - 12 q^{47} - 24 q^{48} - 24 q^{49} - 24 q^{50} + 30 q^{51} - 6 q^{52} - 12 q^{53} + 78 q^{54} - 54 q^{56} - 6 q^{58} - 6 q^{59} + 114 q^{60} - 6 q^{61} - 78 q^{62} - 24 q^{63} - 12 q^{64} - 12 q^{65} - 6 q^{66} - 6 q^{67} + 42 q^{68} - 24 q^{69} - 54 q^{70} - 186 q^{72} - 90 q^{74} - 6 q^{75} - 24 q^{76} - 12 q^{77} - 24 q^{78} - 12 q^{79} - 12 q^{80} - 12 q^{81} - 12 q^{82} - 84 q^{83} + 36 q^{84} - 54 q^{85} + 114 q^{86} - 6 q^{88} + 30 q^{90} - 6 q^{91} - 24 q^{92} - 6 q^{93} - 6 q^{94} - 12 q^{95} + 426 q^{96} - 48 q^{97} - 6 q^{98} - 24 q^{99} + O(q^{100}) \)

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.