↑

Properties

Label 2166.2.i
Level $2166$
Weight $2$
Character orbit 2166.i
Rep. character $\chi_{2166}(415,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $336$
Sturm bound $760$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2166.i (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(760\)

Dimensions

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

Total New Old
Modular forms 2520 336 2184
Cusp forms 2040 336 1704
Eisenstein series 480 0 480

Trace form

\( 336 q - 24 q^{7} + O(q^{10}) \) \( 336 q - 24 q^{7} - 24 q^{11} + 24 q^{14} + 24 q^{15} + 12 q^{17} + 48 q^{20} + 24 q^{21} - 24 q^{22} - 12 q^{25} + 12 q^{26} + 12 q^{31} - 12 q^{33} - 12 q^{34} + 12 q^{35} + 12 q^{41} - 12 q^{42} + 24 q^{43} - 12 q^{44} - 24 q^{45} - 12 q^{46} - 12 q^{47} - 168 q^{49} - 48 q^{53} - 24 q^{56} + 48 q^{58} - 36 q^{59} - 12 q^{60} + 24 q^{61} - 36 q^{62} - 168 q^{64} + 12 q^{65} - 24 q^{68} - 24 q^{69} - 24 q^{70} - 60 q^{71} - 48 q^{73} - 36 q^{74} + 24 q^{77} - 24 q^{78} + 24 q^{79} + 36 q^{82} + 24 q^{83} - 12 q^{84} + 24 q^{85} + 24 q^{86} + 12 q^{87} - 12 q^{88} + 36 q^{89} + 36 q^{91} + 36 q^{92} - 36 q^{93} + 72 q^{94} + 24 q^{97} + 72 q^{98} - 12 q^{99} + O(q^{100}) \)

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

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