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Properties

Label 1728.4.bx
Level $1728$
Weight $4$
Character orbit 1728.bx
Rep. character $\chi_{1728}(35,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $4576$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1728.bx (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 576 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1728, [\chi])\).

Total New Old
Modular forms 13920 4640 9280
Cusp forms 13728 4576 9152
Eisenstein series 192 64 128

Trace form

\( 4576 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} + O(q^{10}) \) \( 4576 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 8 q^{16} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 16 q^{31} + 24 q^{32} - 8 q^{34} - 32 q^{37} + 24 q^{38} - 8 q^{40} + 24 q^{41} - 8 q^{43} - 32 q^{46} + 24 q^{47} - 8 q^{49} + 24 q^{50} - 8 q^{52} - 32 q^{55} + 24 q^{56} - 2384 q^{58} + 24 q^{59} - 8 q^{61} - 32 q^{64} + 48 q^{65} - 8 q^{67} + 24 q^{68} - 8 q^{70} - 32 q^{73} + 24 q^{74} - 4472 q^{76} + 24 q^{77} - 8 q^{79} - 32 q^{82} + 24 q^{83} - 8 q^{85} + 24 q^{86} - 8 q^{88} - 32 q^{91} - 37824 q^{92} - 8 q^{94} + 48 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)