Properties

Label 2366.2.bv
Level $2366$
Weight $2$
Character orbit 2366.bv
Rep. character $\chi_{2366}(95,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2928$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.bv (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 8832 2928 5904
Cusp forms 8640 2928 5712
Eisenstein series 192 0 192

Trace form

\( 2928q - 2q^{3} + 244q^{4} - 2q^{7} + 128q^{9} + O(q^{10}) \) \( 2928q - 2q^{3} + 244q^{4} - 2q^{7} + 128q^{9} + 4q^{10} + 6q^{11} + 2q^{12} + 72q^{13} + 2q^{14} + 64q^{15} - 244q^{16} - 16q^{17} - 24q^{18} + 24q^{19} + 14q^{21} - 8q^{23} - 126q^{25} - 6q^{26} + 16q^{27} + 2q^{28} - 4q^{29} + 100q^{30} + 6q^{31} - 12q^{33} - 6q^{35} - 128q^{36} + 12q^{38} + 82q^{39} - 4q^{40} - 18q^{41} + 4q^{42} - 4q^{43} - 6q^{44} - 18q^{47} - 2q^{48} + 42q^{49} + 12q^{50} + 8q^{51} + 6q^{52} + 106q^{53} - 78q^{54} + 6q^{55} - 2q^{56} + 76q^{58} - 12q^{60} - 10q^{61} + 22q^{62} - 180q^{63} + 244q^{64} + 6q^{65} - 32q^{66} + 60q^{67} + 16q^{68} + 26q^{69} - 264q^{70} + 174q^{71} + 24q^{72} + 72q^{73} - 80q^{74} + 76q^{75} - 50q^{76} - 22q^{77} - 20q^{78} - 38q^{79} + 130q^{81} + 16q^{82} - 14q^{84} - 92q^{85} + 36q^{86} - 64q^{87} - 40q^{90} + 38q^{91} + 8q^{92} - 364q^{93} - 14q^{94} + 96q^{95} - 24q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)