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Properties

Label 3024.2.dl
Level $3024$
Weight $2$
Character orbit 3024.dl
Rep. character $\chi_{3024}(193,\cdot)$
Character field $\Q(\zeta_{9})$
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.dl (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
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

\( 852 q + 3 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{9} + O(q^{10}) \) \( 852 q + 3 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{9} + 3 q^{11} - 12 q^{13} + 12 q^{15} + 3 q^{17} - 3 q^{19} - 6 q^{21} + 3 q^{23} - 3 q^{25} + 12 q^{27} + 3 q^{31} - 3 q^{33} + 3 q^{35} - 6 q^{37} + 39 q^{39} - 12 q^{41} + 12 q^{43} + 9 q^{45} + 3 q^{47} - 6 q^{49} - 15 q^{51} - 6 q^{53} + 24 q^{55} - 21 q^{57} + 3 q^{59} - 3 q^{61} - 24 q^{63} + 45 q^{65} + 3 q^{67} + 12 q^{69} + 6 q^{71} - 6 q^{73} + 3 q^{75} - 30 q^{77} + 3 q^{79} + 45 q^{81} + 42 q^{83} - 27 q^{85} + 3 q^{87} + 3 q^{89} + 3 q^{91} - 3 q^{93} - 81 q^{95} - 12 q^{97} + 120 q^{99} + O(q^{100}) \)

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.

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

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