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Properties

Label 2368.2.cd
Level $2368$
Weight $2$
Character orbit 2368.cd
Rep. character $\chi_{2368}(339,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2416$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.cd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2368 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(608\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2368, [\chi])\).

Total New Old
Modular forms 2448 2448 0
Cusp forms 2416 2416 0
Eisenstein series 32 32 0

Trace form

\( 2416 q - 8 q^{2} - 8 q^{5} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9} + O(q^{10}) \) \( 2416 q - 8 q^{2} - 8 q^{5} - 8 q^{6} - 16 q^{7} - 8 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 16 q^{16} + 32 q^{18} - 8 q^{19} - 8 q^{20} - 16 q^{22} - 24 q^{23} - 48 q^{24} - 16 q^{26} - 8 q^{29} - 32 q^{30} - 16 q^{31} + 32 q^{32} - 16 q^{34} - 8 q^{35} - 8 q^{37} - 16 q^{38} - 8 q^{39} - 64 q^{40} - 48 q^{42} + 8 q^{43} - 16 q^{44} - 32 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{49} - 8 q^{50} + 16 q^{51} - 8 q^{52} - 16 q^{53} - 8 q^{54} - 8 q^{55} + 48 q^{56} - 8 q^{57} + 64 q^{58} - 8 q^{59} - 192 q^{60} - 8 q^{61} + 40 q^{66} + 16 q^{68} - 8 q^{69} - 16 q^{70} - 16 q^{71} - 8 q^{72} - 40 q^{74} - 16 q^{75} - 72 q^{76} + 56 q^{80} - 16 q^{81} + 72 q^{82} - 16 q^{83} - 240 q^{84} + 80 q^{85} - 16 q^{86} - 120 q^{87} - 8 q^{89} - 16 q^{90} - 8 q^{91} + 152 q^{92} + 16 q^{93} - 48 q^{94} + 136 q^{96} + 64 q^{98} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2368, [\chi])\) into newform subspaces

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