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Properties

Label 128.9.l
Level $128$
Weight $9$
Character orbit 128.l
Rep. character $\chi_{128}(3,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $2032$
Sturm bound $144$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 128.l (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(128, [\chi])\).

Total New Old
Modular forms 2064 2064 0
Cusp forms 2032 2032 0
Eisenstein series 32 32 0

Trace form

\( 2032 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} + O(q^{10}) \) \( 2032 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 10290368 q^{50} - 16 q^{51} + 91896272 q^{52} - 16 q^{53} - 158723728 q^{54} - 16 q^{55} - 113749792 q^{56} - 16 q^{57} + 101752544 q^{58} - 16 q^{59} + 327416240 q^{60} - 16 q^{61} + 87863312 q^{62} - 32 q^{63} - 193535824 q^{64} - 454631632 q^{66} - 16 q^{67} - 163729456 q^{68} - 16 q^{69} + 185779760 q^{70} - 16 q^{71} + 522465536 q^{72} - 16 q^{73} + 340057856 q^{74} - 16 q^{75} - 318607760 q^{76} - 16 q^{77} - 735959536 q^{78} - 16 q^{79} + 404319008 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

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