Properties

Label 3024.2.du
Level $3024$
Weight $2$
Character orbit 3024.du
Rep. character $\chi_{3024}(341,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $752$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.du (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

\( 752 q - 4 q^{4} + 6 q^{5} + O(q^{10}) \) \( 752 q - 4 q^{4} + 6 q^{5} - 12 q^{10} + 6 q^{11} + 6 q^{14} - 4 q^{16} - 12 q^{19} - 4 q^{22} + 12 q^{29} + 12 q^{34} + 30 q^{35} - 4 q^{37} + 6 q^{38} - 6 q^{40} - 4 q^{43} + 66 q^{44} - 12 q^{46} + 24 q^{47} - 4 q^{49} + 12 q^{50} - 6 q^{52} + 48 q^{56} + 2 q^{58} + 12 q^{59} - 24 q^{62} - 16 q^{64} - 4 q^{67} + 6 q^{68} + 26 q^{70} - 78 q^{74} + 6 q^{77} - 8 q^{79} - 24 q^{82} - 60 q^{83} + 6 q^{85} + 66 q^{86} + 2 q^{88} + 20 q^{91} + 12 q^{92} + 90 q^{98} + O(q^{100}) \)

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

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