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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

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

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

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