Properties

Label 2366.2.bw
Level $2366$
Weight $2$
Character orbit 2366.bw
Rep. character $\chi_{2366}(25,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2880$
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.bw (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 2880 5952
Cusp forms 8640 2880 5760
Eisenstein series 192 0 192

Trace form

\( 2880q - 120q^{4} + 108q^{9} + O(q^{10}) \) \( 2880q - 120q^{4} + 108q^{9} + 4q^{10} + 48q^{13} - 4q^{14} - 104q^{15} + 120q^{16} + 8q^{17} - 8q^{23} - 112q^{25} + 6q^{26} - 16q^{29} - 44q^{30} + 48q^{35} + 216q^{36} + 12q^{38} - 28q^{39} - 4q^{40} + 4q^{42} - 8q^{43} - 44q^{49} + 8q^{51} - 2q^{52} + 100q^{53} - 78q^{54} + 24q^{55} - 8q^{56} + 52q^{58} + 12q^{61} - 8q^{62} - 130q^{63} + 240q^{64} - 24q^{65} + 16q^{66} + 156q^{67} - 8q^{68} + 8q^{69} + 156q^{71} - 80q^{74} + 434q^{75} + 52q^{76} - 28q^{77} - 32q^{78} + 20q^{79} + 104q^{81} - 8q^{82} + 208q^{85} + 78q^{86} - 64q^{87} - 40q^{90} - 96q^{91} - 16q^{92} - 20q^{94} + 96q^{95} - 156q^{97} + O(q^{100}) \)

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

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