Properties

Label 2366.2.bi
Level $2366$
Weight $2$
Character orbit 2366.bi
Rep. character $\chi_{2366}(9,\cdot)$
Character field $\Q(\zeta_{39})$
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.bi (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{39})\)
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

\( 2928q - 4q^{3} + 122q^{4} + 6q^{7} - 240q^{9} + O(q^{10}) \) \( 2928q - 4q^{3} + 122q^{4} + 6q^{7} - 240q^{9} - 8q^{10} - 20q^{11} + 2q^{12} - 72q^{13} - 2q^{14} - 48q^{15} + 122q^{16} + 8q^{17} + 6q^{21} - 4q^{23} + 126q^{25} - 6q^{26} - 16q^{27} - 12q^{28} - 4q^{29} - 44q^{30} + 22q^{31} + 32q^{33} + 18q^{35} + 120q^{36} - 20q^{37} + 12q^{38} - 50q^{39} + 4q^{40} + 2q^{41} - 10q^{42} - 12q^{43} + 10q^{44} - 20q^{45} - 8q^{46} - 6q^{47} + 2q^{48} - 26q^{49} - 12q^{50} + 214q^{53} + 84q^{54} + 6q^{55} - 2q^{56} + 28q^{57} + 104q^{58} + 8q^{59} + 4q^{60} - 20q^{61} + 22q^{62} + 284q^{63} - 244q^{64} + 50q^{65} + 16q^{66} - 260q^{67} + 8q^{68} + 34q^{69} + 64q^{70} - 130q^{71} - 28q^{73} + 208q^{74} + 832q^{75} + 26q^{76} - 10q^{77} + 12q^{78} + 14q^{79} - 212q^{81} - 32q^{82} - 84q^{83} - 124q^{85} - 166q^{86} + 8q^{87} + 14q^{89} - 40q^{90} - 100q^{91} + 8q^{92} - 342q^{93} - 68q^{94} - 100q^{95} + 44q^{97} + 36q^{98} - 52q^{99} + O(q^{100}) \)

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

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