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Properties

Label 2166.4.e
Level $2166$
Weight $4$
Character orbit 2166.e
Rep. character $\chi_{2166}(1375,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $340$
Sturm bound $1520$

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Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2166.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2166, [\chi])\).

Total New Old
Modular forms 2360 340 2020
Cusp forms 2200 340 1860
Eisenstein series 160 0 160

Trace form

\( 340 q - 6 q^{3} - 680 q^{4} + 32 q^{5} + 4 q^{7} - 1530 q^{9} + O(q^{10}) \) \( 340 q - 6 q^{3} - 680 q^{4} + 32 q^{5} + 4 q^{7} - 1530 q^{9} + 40 q^{10} + 280 q^{11} + 48 q^{12} + 174 q^{13} + 88 q^{14} - 24 q^{15} - 2720 q^{16} - 324 q^{17} - 256 q^{20} + 78 q^{21} + 72 q^{22} + 40 q^{23} - 4766 q^{25} + 688 q^{26} + 108 q^{27} - 8 q^{28} - 52 q^{29} - 48 q^{30} - 188 q^{31} + 324 q^{33} + 152 q^{34} - 796 q^{35} - 6120 q^{36} - 1060 q^{37} - 252 q^{39} + 160 q^{40} - 248 q^{41} - 24 q^{42} - 2 q^{43} - 560 q^{44} - 576 q^{45} - 576 q^{46} - 812 q^{47} - 96 q^{48} + 17008 q^{49} + 320 q^{50} + 204 q^{51} + 696 q^{52} - 1996 q^{53} - 2412 q^{55} - 704 q^{56} - 1888 q^{58} + 488 q^{59} - 96 q^{60} - 786 q^{61} + 248 q^{62} - 18 q^{63} + 21760 q^{64} + 1328 q^{65} + 240 q^{66} - 34 q^{67} + 2592 q^{68} - 2952 q^{69} + 1128 q^{70} + 848 q^{71} - 90 q^{73} + 264 q^{74} + 2004 q^{75} - 2144 q^{77} - 24 q^{78} + 2470 q^{79} + 512 q^{80} - 13770 q^{81} - 824 q^{82} + 5840 q^{83} - 624 q^{84} + 724 q^{85} + 944 q^{86} + 1320 q^{87} - 576 q^{88} + 2456 q^{89} + 360 q^{90} + 106 q^{91} + 160 q^{92} + 90 q^{93} - 5952 q^{94} + 1260 q^{97} - 4592 q^{98} - 1260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2166, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2166, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2166, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(722, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1083, [\chi])\)\(^{\oplus 2}\)