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Properties

Label 1728.4.ch
Level $1728$
Weight $4$
Character orbit 1728.ch
Rep. character $\chi_{1728}(11,\cdot)$
Character field $\Q(\zeta_{144})$
Dimension $41376$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1728.ch (of order \(144\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1728 \)
Character field: \(\Q(\zeta_{144})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 41568 41568 0
Cusp forms 41376 41376 0
Eisenstein series 192 192 0

Trace form

\( 41376 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 48 q^{6} - 48 q^{7} - 72 q^{8} - 48 q^{9} + O(q^{10}) \) \( 41376 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 48 q^{6} - 48 q^{7} - 72 q^{8} - 48 q^{9} - 24 q^{10} - 48 q^{11} - 48 q^{12} - 48 q^{13} - 48 q^{14} - 48 q^{15} - 48 q^{16} - 72 q^{17} - 48 q^{18} - 24 q^{19} - 48 q^{20} - 48 q^{21} - 48 q^{22} - 48 q^{23} + 2952 q^{24} - 48 q^{25} - 48 q^{27} - 96 q^{28} - 48 q^{29} - 48 q^{30} - 96 q^{31} - 48 q^{32} - 48 q^{34} - 72 q^{35} - 48 q^{36} - 24 q^{37} - 48 q^{38} - 48 q^{39} - 48 q^{40} - 48 q^{41} - 19008 q^{42} - 48 q^{43} - 72 q^{44} - 48 q^{45} - 24 q^{46} - 48 q^{47} - 48 q^{48} - 48 q^{49} - 48 q^{50} - 48 q^{51} - 48 q^{52} - 48 q^{54} - 96 q^{55} - 48 q^{56} - 48 q^{57} + 7080 q^{58} - 48 q^{59} - 48 q^{60} - 48 q^{61} - 72 q^{62} - 24 q^{64} - 96 q^{65} - 48 q^{66} - 48 q^{67} - 48 q^{68} - 48 q^{69} - 48 q^{70} - 72 q^{71} - 48 q^{72} - 24 q^{73} - 48 q^{74} - 48 q^{75} - 48 q^{76} - 48 q^{77} - 48 q^{78} - 48 q^{79} - 48 q^{81} - 96 q^{82} - 48 q^{83} - 48 q^{84} - 48 q^{85} - 48 q^{86} - 48 q^{87} - 48 q^{88} - 72 q^{89} - 48 q^{90} - 24 q^{91} - 37896 q^{92} - 48 q^{93} - 48 q^{94} - 96 q^{95} - 48 q^{96} - 72 q^{98} - 48 q^{99} + O(q^{100}) \)

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.