Properties

Label 288.8.bf
Level $288$
Weight $8$
Character orbit 288.bf
Rep. character $\chi_{288}(11,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $2672$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 288.bf (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(288, [\chi])\).

Total New Old
Modular forms 2704 2704 0
Cusp forms 2672 2672 0
Eisenstein series 32 32 0

Trace form

\( 2672 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 2672 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} - 598048 q^{24} - 4 q^{25} + 476080 q^{27} - 16 q^{28} - 12 q^{29} + 869440 q^{30} - 12 q^{32} - 16 q^{33} - 516 q^{34} - 2399820 q^{36} - 16 q^{37} - 12 q^{38} - 283952 q^{39} - 4 q^{40} - 12 q^{41} - 6854408 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} + 5044356 q^{48} + 1485264 q^{50} - 17504 q^{51} - 4 q^{52} - 7445644 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 5179064 q^{58} - 12 q^{59} + 8664076 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} + 30004792 q^{66} - 4 q^{67} - 196620 q^{68} - 8 q^{69} - 4 q^{70} + 24248212 q^{72} - 16 q^{73} - 12 q^{74} - 312508 q^{75} + 14603588 q^{76} - 12 q^{77} - 13647424 q^{78} - 8 q^{79} - 16 q^{82} + 28697628 q^{83} - 24732392 q^{84} - 312504 q^{85} - 12 q^{86} - 40789120 q^{87} - 4 q^{88} + 35949652 q^{90} - 16 q^{91} - 81661176 q^{92} - 8756 q^{93} - 1028 q^{94} - 83848996 q^{96} - 8 q^{97} + 9729720 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

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