↑

Properties

Label 1728.3.bw
Level $1728$
Weight $3$
Character orbit 1728.bw
Rep. character $\chi_{1728}(19,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $3040$
Sturm bound $864$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.bw (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).

Total New Old
Modular forms 9312 3104 6208
Cusp forms 9120 3040 6080
Eisenstein series 192 64 128

Trace form

\( 3040 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 32 q^{8} + O(q^{10}) \) \( 3040 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 32 q^{8} - 32 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 32 q^{17} - 32 q^{19} + 8 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} + 32 q^{26} - 32 q^{28} + 8 q^{29} - 16 q^{31} + 8 q^{32} - 8 q^{34} + 32 q^{35} - 32 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 8 q^{43} + 32 q^{44} - 32 q^{46} + 8 q^{47} - 8 q^{49} + 8 q^{50} - 8 q^{52} + 32 q^{53} - 32 q^{55} + 8 q^{56} + 352 q^{58} + 8 q^{59} - 8 q^{61} - 32 q^{62} - 32 q^{64} + 16 q^{65} - 8 q^{67} + 8 q^{68} - 8 q^{70} + 32 q^{71} - 32 q^{73} + 8 q^{74} + 616 q^{76} + 8 q^{77} - 8 q^{79} - 1888 q^{80} - 32 q^{82} + 8 q^{83} - 8 q^{85} - 1864 q^{86} - 8 q^{88} + 32 q^{89} - 32 q^{91} + 464 q^{92} - 8 q^{94} + 16 q^{95} + 848 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)