Properties

Label 2366.2.bl
Level $2366$
Weight $2$
Character orbit 2366.bl
Rep. character $\chi_{2366}(107,\cdot)$
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.bl (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

\( 2928q + 2q^{3} - 244q^{4} + 6q^{7} + 120q^{9} + O(q^{10}) \) \( 2928q + 2q^{3} - 244q^{4} + 6q^{7} + 120q^{9} + 4q^{10} + 10q^{11} + 2q^{12} - 72q^{13} - 2q^{14} - 48q^{15} - 244q^{16} - 16q^{17} + 6q^{21} + 8q^{23} + 126q^{25} + 6q^{26} - 16q^{27} + 6q^{28} - 4q^{29} + 100q^{30} + 22q^{31} - 16q^{33} - 18q^{35} + 120q^{36} + 40q^{37} + 12q^{38} + 70q^{39} + 4q^{40} + 2q^{41} + 20q^{42} - 12q^{43} + 10q^{44} + 40q^{45} + 16q^{46} - 6q^{47} + 2q^{48} - 14q^{49} - 12q^{50} + 6q^{52} - 98q^{53} + 66q^{54} + 6q^{55} - 2q^{56} + 28q^{57} - 52q^{58} - 16q^{59} + 4q^{60} + 10q^{61} + 22q^{62} - 196q^{63} - 244q^{64} + 2q^{65} + 16q^{66} + 208q^{67} - 16q^{68} + 34q^{69} + 64q^{70} - 130q^{71} - 28q^{73} - 104q^{74} - 572q^{75} + 26q^{76} - 10q^{77} + 12q^{78} + 14q^{79} + 106q^{81} + 16q^{82} - 84q^{83} + 6q^{84} - 124q^{85} + 68q^{86} - 16q^{87} - 28q^{89} - 40q^{90} - 58q^{91} + 8q^{92} + 372q^{93} + 34q^{94} - 112q^{95} + 44q^{97} - 48q^{98} - 52q^{99} + O(q^{100}) \)

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

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