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Properties

Label 384.5.x
Level $384$
Weight $5$
Character orbit 384.x
Rep. character $\chi_{384}(5,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $4064$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 384.x (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 384 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(384, [\chi])\).

Total New Old
Modular forms 4128 4128 0
Cusp forms 4064 4064 0
Eisenstein series 64 64 0

Trace form

\( 4064 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} + O(q^{10}) \) \( 4064 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} + 17920 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 131072 q^{58} - 16 q^{60} - 32 q^{61} + 24352 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} + 122272 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 49536 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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