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Properties

Label 2368.2.dw
Level $2368$
Weight $2$
Character orbit 2368.dw
Rep. character $\chi_{2368}(53,\cdot)$
Character field $\Q(\zeta_{144})$
Dimension $14496$
Sturm bound $608$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.dw (of order \(144\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2368 \)
Character field: \(\Q(\zeta_{144})\)
Sturm bound: \(608\)

Dimensions

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

Total New Old
Modular forms 14688 14688 0
Cusp forms 14496 14496 0
Eisenstein series 192 192 0

Trace form

\( 14496 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 96 q^{6} - 48 q^{7} - 24 q^{8} - 48 q^{9} + O(q^{10}) \) \( 14496 q - 48 q^{2} - 48 q^{3} - 48 q^{4} - 48 q^{5} - 96 q^{6} - 48 q^{7} - 24 q^{8} - 48 q^{9} - 24 q^{10} - 24 q^{11} - 48 q^{12} - 48 q^{13} - 24 q^{14} - 48 q^{15} - 48 q^{16} - 48 q^{17} - 48 q^{18} - 48 q^{19} - 48 q^{20} - 48 q^{21} - 48 q^{22} - 24 q^{23} - 168 q^{24} - 48 q^{25} - 24 q^{26} - 24 q^{27} - 48 q^{28} - 24 q^{29} - 48 q^{30} + 192 q^{32} - 168 q^{34} - 48 q^{35} - 96 q^{36} - 48 q^{37} - 96 q^{38} - 48 q^{39} - 48 q^{40} - 48 q^{41} - 48 q^{42} - 96 q^{43} - 48 q^{44} - 24 q^{45} - 48 q^{46} - 24 q^{47} - 24 q^{48} - 48 q^{49} - 48 q^{50} - 24 q^{51} - 48 q^{52} - 48 q^{53} - 48 q^{54} - 48 q^{55} - 48 q^{56} - 48 q^{57} - 48 q^{58} - 48 q^{59} + 552 q^{60} - 48 q^{61} + 48 q^{62} - 528 q^{63} - 24 q^{64} - 96 q^{65} - 24 q^{66} - 48 q^{67} - 672 q^{68} - 48 q^{69} - 624 q^{70} - 48 q^{71} - 48 q^{72} - 96 q^{73} + 120 q^{74} - 96 q^{75} - 48 q^{76} - 48 q^{77} - 48 q^{78} - 48 q^{79} - 96 q^{80} - 48 q^{81} - 24 q^{82} - 48 q^{83} + 312 q^{84} - 24 q^{85} - 360 q^{86} - 48 q^{87} - 24 q^{88} - 48 q^{89} - 48 q^{90} - 48 q^{91} - 504 q^{92} + 96 q^{93} - 48 q^{94} - 48 q^{96} - 48 q^{98} - 48 q^{99} + O(q^{100}) \)

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.