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Properties

Label 2304.2.cd
Level $2304$
Weight $2$
Character orbit 2304.cd
Rep. character $\chi_{2304}(11,\cdot)$
Character field $\Q(\zeta_{192})$
Dimension $24448$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2304.cd (of order \(192\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2304 \)
Character field: \(\Q(\zeta_{192})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

Total New Old
Modular forms 24704 24704 0
Cusp forms 24448 24448 0
Eisenstein series 256 256 0

Trace form

\( 24448 q - 96 q^{2} - 64 q^{3} - 32 q^{4} - 96 q^{5} - 64 q^{6} - 32 q^{7} - 64 q^{9} + O(q^{10}) \) \( 24448 q - 96 q^{2} - 64 q^{3} - 32 q^{4} - 96 q^{5} - 64 q^{6} - 32 q^{7} - 64 q^{9} - 128 q^{10} - 96 q^{11} - 64 q^{12} - 32 q^{13} - 96 q^{14} - 64 q^{15} - 32 q^{16} - 64 q^{18} - 128 q^{19} - 96 q^{20} - 64 q^{21} - 32 q^{22} - 96 q^{23} - 64 q^{24} - 32 q^{25} - 64 q^{27} - 128 q^{28} - 96 q^{29} - 64 q^{30} - 32 q^{31} - 96 q^{32} - 64 q^{33} - 32 q^{34} - 64 q^{36} - 128 q^{37} - 96 q^{38} - 64 q^{39} - 32 q^{40} - 96 q^{41} - 64 q^{42} - 32 q^{43} - 64 q^{45} - 128 q^{46} - 96 q^{47} - 64 q^{48} - 32 q^{49} - 96 q^{50} - 64 q^{51} - 32 q^{52} - 64 q^{54} - 128 q^{55} - 96 q^{56} - 64 q^{57} - 32 q^{58} - 96 q^{59} - 64 q^{60} - 32 q^{61} - 64 q^{63} - 128 q^{64} - 96 q^{65} - 64 q^{66} - 32 q^{67} - 96 q^{68} - 64 q^{69} - 32 q^{70} - 64 q^{72} - 128 q^{73} - 96 q^{74} - 64 q^{75} - 32 q^{76} - 96 q^{77} - 64 q^{78} - 32 q^{79} - 64 q^{81} - 128 q^{82} - 96 q^{83} - 64 q^{84} - 32 q^{85} - 96 q^{86} - 64 q^{87} - 32 q^{88} - 64 q^{90} - 128 q^{91} - 96 q^{92} - 64 q^{93} - 32 q^{94} - 96 q^{95} - 64 q^{96} - 32 q^{97} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

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