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Properties

Label 320.4.bd
Level $320$
Weight $4$
Character orbit 320.bd
Rep. character $\chi_{320}(43,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1136$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 320.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 320 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(320, [\chi])\).

Total New Old
Modular forms 1168 1168 0
Cusp forms 1136 1136 0
Eisenstein series 32 32 0

Trace form

\( 1136 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 8 q^{8} + O(q^{10}) \) \( 1136 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{10} - 16 q^{11} - 104 q^{12} - 8 q^{13} - 416 q^{14} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 8 q^{20} - 16 q^{21} - 872 q^{22} - 8 q^{23} - 912 q^{24} - 8 q^{25} - 16 q^{26} - 8 q^{27} - 8 q^{28} + 2376 q^{30} - 32 q^{31} - 8 q^{32} + 128 q^{34} - 8 q^{35} - 16 q^{36} - 8 q^{37} - 2416 q^{38} - 2224 q^{40} - 16 q^{41} - 8 q^{42} - 8 q^{43} - 224 q^{45} - 16 q^{46} - 16 q^{47} - 4896 q^{48} - 4272 q^{50} - 2992 q^{51} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 688 q^{56} - 8 q^{57} - 4040 q^{58} - 6112 q^{60} - 16 q^{61} - 72 q^{62} - 16 q^{65} - 5488 q^{66} - 8 q^{67} + 3472 q^{68} + 2112 q^{69} - 8 q^{70} + 432 q^{71} + 2752 q^{72} - 8 q^{73} - 8 q^{75} + 5936 q^{76} - 8 q^{77} + 11696 q^{78} + 5664 q^{79} - 8 q^{80} - 16 q^{81} - 12808 q^{82} - 8 q^{83} + 992 q^{85} - 16 q^{86} + 2568 q^{87} - 624 q^{88} - 8 q^{90} - 16 q^{91} + 7064 q^{92} - 224 q^{93} - 128 q^{94} - 16 q^{95} - 16 q^{96} - 6384 q^{98} + 10624 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

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