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Properties

Label 2166.2.m
Level $2166$
Weight $2$
Character orbit 2166.m
Rep. character $\chi_{2166}(115,\cdot)$
Character field $\Q(\zeta_{19})$
Dimension $1116$
Sturm bound $760$

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Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2166.m (of order \(19\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 361 \)
Character field: \(\Q(\zeta_{19})\)
Sturm bound: \(760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2166, [\chi])\).

Total New Old
Modular forms 6912 1116 5796
Cusp forms 6768 1116 5652
Eisenstein series 144 0 144

Trace form

\( 1116 q + 2 q^{3} - 62 q^{4} + 4 q^{7} - 62 q^{9} + O(q^{10}) \) \( 1116 q + 2 q^{3} - 62 q^{4} + 4 q^{7} - 62 q^{9} + 4 q^{10} + 8 q^{11} + 2 q^{12} + 16 q^{13} - 60 q^{14} + 8 q^{15} - 62 q^{16} - 136 q^{17} + 18 q^{19} + 16 q^{21} - 56 q^{22} + 32 q^{23} - 22 q^{25} + 16 q^{26} + 2 q^{27} + 4 q^{28} - 120 q^{29} + 8 q^{30} + 20 q^{31} - 64 q^{33} + 16 q^{34} + 40 q^{35} - 62 q^{36} + 40 q^{37} + 20 q^{38} + 20 q^{39} + 4 q^{40} + 16 q^{41} + 8 q^{42} - 138 q^{43} + 8 q^{44} - 44 q^{46} + 32 q^{47} + 2 q^{48} - 94 q^{49} - 120 q^{50} + 4 q^{51} + 16 q^{52} + 56 q^{53} + 72 q^{55} - 60 q^{56} + 18 q^{57} + 16 q^{58} + 56 q^{59} + 8 q^{60} + 36 q^{61} + 32 q^{62} + 4 q^{63} - 62 q^{64} - 224 q^{65} + 72 q^{67} + 16 q^{68} - 128 q^{69} - 104 q^{70} + 80 q^{71} + 60 q^{73} - 52 q^{74} + 30 q^{75} - 58 q^{76} + 72 q^{77} + 20 q^{78} + 84 q^{79} - 62 q^{81} - 44 q^{82} + 96 q^{83} + 16 q^{84} + 112 q^{85} - 44 q^{86} + 16 q^{87} + 20 q^{88} + 28 q^{89} + 4 q^{90} + 20 q^{91} + 32 q^{92} + 36 q^{93} - 20 q^{94} - 340 q^{95} - 120 q^{97} + 64 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2166, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2166, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2166, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(722, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1083, [\chi])\)\(^{\oplus 2}\)