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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

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

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

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