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Properties

Label 3584.2.ck
Level $3584$
Weight $2$
Character orbit 3584.ck
Rep. character $\chi_{3584}(3,\cdot)$
Character field $\Q(\zeta_{384})$
Dimension $65280$
Sturm bound $1024$

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Defining parameters

Level: \( N \) \(=\) \( 3584 = 2^{9} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3584.ck (of order \(384\) and degree \(128\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3584 \)
Character field: \(\Q(\zeta_{384})\)
Sturm bound: \(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3584, [\chi])\).

Total New Old
Modular forms 65792 65792 0
Cusp forms 65280 65280 0
Eisenstein series 512 512 0

Trace form

\( 65280 q - 64 q^{2} - 192 q^{3} - 64 q^{4} - 192 q^{5} - 128 q^{7} - 256 q^{8} - 64 q^{9} + O(q^{10}) \) \( 65280 q - 64 q^{2} - 192 q^{3} - 64 q^{4} - 192 q^{5} - 128 q^{7} - 256 q^{8} - 64 q^{9} - 192 q^{10} - 64 q^{11} - 192 q^{12} - 128 q^{14} - 256 q^{15} - 64 q^{16} - 192 q^{17} - 64 q^{18} - 192 q^{19} - 128 q^{21} - 256 q^{22} - 64 q^{23} - 192 q^{24} - 64 q^{25} - 192 q^{26} - 128 q^{28} - 256 q^{29} - 64 q^{30} - 192 q^{31} - 64 q^{32} - 192 q^{33} - 128 q^{35} - 256 q^{36} - 64 q^{37} - 192 q^{38} - 64 q^{39} - 192 q^{40} - 128 q^{42} - 256 q^{43} - 64 q^{44} - 192 q^{45} - 64 q^{46} - 192 q^{47} - 128 q^{49} - 256 q^{50} - 64 q^{51} - 192 q^{52} - 64 q^{53} - 192 q^{54} - 128 q^{56} - 256 q^{57} - 64 q^{58} - 192 q^{59} - 64 q^{60} - 192 q^{61} - 128 q^{63} - 256 q^{64} - 64 q^{65} - 192 q^{66} - 64 q^{67} - 192 q^{68} - 128 q^{70} - 256 q^{71} - 64 q^{72} - 192 q^{73} - 64 q^{74} - 192 q^{75} - 128 q^{77} - 256 q^{78} - 64 q^{79} - 192 q^{80} - 64 q^{81} - 192 q^{82} - 128 q^{84} - 256 q^{85} - 64 q^{86} - 192 q^{87} - 64 q^{88} - 192 q^{89} - 128 q^{91} - 256 q^{92} - 64 q^{93} - 192 q^{94} - 64 q^{95} - 192 q^{96} - 128 q^{98} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

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