Properties

Label 3024.2.gg
Level 3024
Weight 2
Character orbit gg
Rep. character \(\chi_{3024}(257,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 852
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.gg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
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 876 2652
Cusp forms 3384 852 2532
Eisenstein series 144 24 120

Trace form

\( 852q + 9q^{3} - 9q^{5} + 6q^{7} - 3q^{9} + O(q^{10}) \) \( 852q + 9q^{3} - 9q^{5} + 6q^{7} - 3q^{9} + 3q^{11} + 12q^{15} - 18q^{17} - 6q^{21} + 3q^{23} - 3q^{25} - 24q^{29} + 9q^{31} - 9q^{33} + 9q^{35} + 3q^{37} - 69q^{39} + 12q^{43} - 9q^{45} + 9q^{47} - 6q^{49} + 39q^{51} - 3q^{57} + 9q^{59} - 9q^{61} + 36q^{63} - 27q^{65} + 3q^{67} - 72q^{69} + 18q^{71} - 9q^{73} + 9q^{75} + 18q^{77} + 3q^{79} + 21q^{81} + 90q^{83} - 27q^{85} + 9q^{87} - 18q^{89} + 3q^{91} - 3q^{93} - 3q^{95} + 120q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database