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Properties

Label 2366.2.bk
Level $2366$
Weight $2$
Character orbit 2366.bk
Rep. character $\chi_{2366}(53,\cdot)$
Character field $\Q(\zeta_{39})$
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.bk (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 2880 5952
Cusp forms 8640 2880 5760
Eisenstein series 192 0 192

Trace form

\( 2880 q + 120 q^{4} - 8 q^{7} + 124 q^{9} + O(q^{10}) \) \( 2880 q + 120 q^{4} - 8 q^{7} + 124 q^{9} + 4 q^{10} + 4 q^{11} - 48 q^{13} + 4 q^{14} + 72 q^{15} + 120 q^{16} + 8 q^{17} - 4 q^{19} + 16 q^{21} + 8 q^{23} + 112 q^{25} - 6 q^{26} + 4 q^{28} - 16 q^{29} - 44 q^{30} + 12 q^{31} - 28 q^{33} - 248 q^{36} + 12 q^{38} - 52 q^{39} + 4 q^{40} + 32 q^{41} + 20 q^{42} - 40 q^{43} + 4 q^{44} + 40 q^{45} + 4 q^{46} + 12 q^{47} + 44 q^{49} - 48 q^{50} + 24 q^{51} - 2 q^{52} - 116 q^{53} + 66 q^{54} + 24 q^{55} - 8 q^{56} - 48 q^{57} - 28 q^{58} + 8 q^{59} + 16 q^{60} - 12 q^{61} - 8 q^{62} - 126 q^{63} - 240 q^{64} - 4 q^{65} + 16 q^{66} + 60 q^{67} + 8 q^{68} + 40 q^{69} - 200 q^{70} - 148 q^{71} + 4 q^{73} - 104 q^{74} - 214 q^{75} - 44 q^{76} - 52 q^{77} + 28 q^{79} + 152 q^{81} - 8 q^{82} + 24 q^{83} - 32 q^{84} + 176 q^{85} + 74 q^{86} - 16 q^{87} - 28 q^{89} - 40 q^{90} + 120 q^{91} - 16 q^{92} - 20 q^{93} - 20 q^{94} - 112 q^{95} - 188 q^{97} + 24 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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