Properties

Label 3024.2.hi
Level 3024
Weight 2
Character orbit hi
Rep. character \(\chi_{3024}(5,\cdot)\)
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.hi (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

\( 6864q - 6q^{2} - 18q^{3} - 6q^{4} - 18q^{5} - 36q^{8} + O(q^{10}) \) \( 6864q - 6q^{2} - 18q^{3} - 6q^{4} - 18q^{5} - 36q^{8} - 6q^{11} - 18q^{12} - 12q^{14} - 48q^{15} - 6q^{16} - 72q^{17} - 6q^{18} - 12q^{21} - 24q^{22} - 18q^{24} - 24q^{28} - 24q^{29} - 6q^{30} - 36q^{31} - 6q^{32} - 36q^{33} - 36q^{34} - 18q^{35} - 24q^{36} + 6q^{37} - 18q^{38} - 18q^{40} - 42q^{42} - 24q^{43} - 18q^{44} - 18q^{45} + 6q^{46} - 36q^{47} - 24q^{49} - 24q^{50} - 78q^{51} - 18q^{52} - 270q^{54} + 30q^{56} - 6q^{58} - 18q^{59} + 54q^{60} - 18q^{61} + 198q^{62} - 24q^{63} - 12q^{64} - 12q^{65} - 18q^{66} - 6q^{67} - 18q^{68} - 96q^{70} + 114q^{72} - 174q^{74} - 18q^{75} - 12q^{77} - 24q^{78} - 12q^{79} - 12q^{81} - 36q^{82} - 180q^{83} - 174q^{84} - 54q^{85} - 66q^{86} - 6q^{88} - 162q^{90} - 6q^{91} - 24q^{92} - 6q^{93} - 18q^{94} - 12q^{95} - 18q^{96} - 18q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database