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Properties

Label 1152.3.bu
Level $1152$
Weight $3$
Character orbit 1152.bu
Rep. character $\chi_{1152}(43,\cdot)$
Character field $\Q(\zeta_{96})$
Dimension $12224$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.bu (of order \(96\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1152 \)
Character field: \(\Q(\zeta_{96})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

Total New Old
Modular forms 12352 12352 0
Cusp forms 12224 12224 0
Eisenstein series 128 128 0

Trace form

\( 12224 q - 16 q^{2} - 32 q^{3} - 16 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 64 q^{8} - 32 q^{9} + O(q^{10}) \) \( 12224 q - 16 q^{2} - 32 q^{3} - 16 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 64 q^{8} - 32 q^{9} - 64 q^{10} - 16 q^{11} - 32 q^{12} - 16 q^{13} - 16 q^{14} - 32 q^{15} - 16 q^{16} - 64 q^{17} - 32 q^{18} - 64 q^{19} - 16 q^{20} - 32 q^{21} - 16 q^{22} - 16 q^{23} - 32 q^{24} - 16 q^{25} - 64 q^{26} - 32 q^{27} - 64 q^{28} - 16 q^{29} - 32 q^{30} - 16 q^{31} - 16 q^{32} - 32 q^{33} - 16 q^{34} - 64 q^{35} - 32 q^{36} - 64 q^{37} - 16 q^{38} - 32 q^{39} - 16 q^{40} - 16 q^{41} - 32 q^{42} - 16 q^{43} - 64 q^{44} - 32 q^{45} - 64 q^{46} - 16 q^{47} - 32 q^{48} - 16 q^{49} - 16 q^{50} - 32 q^{51} - 16 q^{52} - 64 q^{53} - 32 q^{54} - 64 q^{55} - 16 q^{56} - 32 q^{57} - 736 q^{58} - 16 q^{59} - 32 q^{60} - 16 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 32 q^{66} - 16 q^{67} - 16 q^{68} - 32 q^{69} - 16 q^{70} - 64 q^{71} - 32 q^{72} - 64 q^{73} - 16 q^{74} - 32 q^{75} - 1264 q^{76} - 16 q^{77} - 32 q^{78} - 16 q^{79} - 64 q^{80} - 32 q^{81} - 64 q^{82} - 16 q^{83} - 32 q^{84} - 16 q^{85} - 16 q^{86} - 32 q^{87} - 16 q^{88} - 64 q^{89} - 32 q^{90} - 64 q^{91} - 16 q^{92} - 32 q^{93} - 16 q^{94} - 16 q^{95} - 32 q^{96} - 16 q^{97} - 64 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

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