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Properties

Label 2166.4.i
Level $2166$
Weight $4$
Character orbit 2166.i
Rep. character $\chi_{2166}(415,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $1020$
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.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1520\)

Dimensions

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

Total New Old
Modular forms 7080 1020 6060
Cusp forms 6600 1020 5580
Eisenstein series 480 0 480

Trace form

\( 1020 q - 48 q^{7} + O(q^{10}) \) \( 1020 q - 48 q^{7} - 336 q^{11} + 72 q^{12} - 6 q^{13} + 48 q^{14} - 144 q^{15} - 372 q^{17} - 768 q^{20} - 486 q^{21} + 48 q^{22} + 576 q^{23} + 1068 q^{25} + 456 q^{26} + 162 q^{27} + 264 q^{28} + 936 q^{29} + 60 q^{31} - 576 q^{33} + 360 q^{34} - 2604 q^{35} - 384 q^{37} - 156 q^{41} + 72 q^{42} - 558 q^{43} + 336 q^{44} + 864 q^{45} + 1752 q^{46} + 1416 q^{47} - 23274 q^{49} - 528 q^{52} + 2460 q^{53} - 468 q^{55} + 960 q^{56} - 2592 q^{58} - 2304 q^{59} + 288 q^{60} - 2280 q^{61} - 1656 q^{62} + 108 q^{63} - 32640 q^{64} + 420 q^{65} + 3930 q^{67} - 3072 q^{68} + 1656 q^{69} + 2832 q^{70} - 1308 q^{71} - 282 q^{73} - 792 q^{74} - 6300 q^{75} + 12144 q^{77} + 1008 q^{78} + 5496 q^{79} + 3768 q^{82} - 3012 q^{83} + 1008 q^{84} - 2220 q^{85} - 4416 q^{86} + 684 q^{87} + 1056 q^{88} - 1980 q^{89} - 9396 q^{91} - 4320 q^{92} + 1260 q^{93} - 7152 q^{94} - 2940 q^{97} - 5616 q^{98} + 756 q^{99} + O(q^{100}) \)

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

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