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Properties

Label 2169.2.g
Level $2169$
Weight $2$
Character orbit 2169.g
Rep. character $\chi_{2169}(1189,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $198$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(484\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2169, [\chi])\).

Total New Old
Modular forms 492 202 290
Cusp forms 476 198 278
Eisenstein series 16 4 12

Trace form

\( 198 q + q^{2} - 95 q^{4} + 12 q^{5} + q^{7} + O(q^{10}) \) \( 198 q + q^{2} - 95 q^{4} + 12 q^{5} + q^{7} + 2 q^{10} - q^{13} + 2 q^{14} - 87 q^{16} + 38 q^{17} - 19 q^{19} - 15 q^{20} - 3 q^{22} + 22 q^{23} + 178 q^{25} + 20 q^{26} + 24 q^{28} - 3 q^{29} - 2 q^{31} - 19 q^{32} - 10 q^{34} + 11 q^{35} + 2 q^{37} - 2 q^{38} - 80 q^{40} - 4 q^{41} + 16 q^{43} - 30 q^{44} + 21 q^{46} + 30 q^{47} - 52 q^{49} - 13 q^{50} + 2 q^{52} - 9 q^{53} - 19 q^{55} + 15 q^{56} + 38 q^{58} + 14 q^{59} - 62 q^{61} - 8 q^{62} + 100 q^{64} + 19 q^{65} + 24 q^{67} - 63 q^{68} + 36 q^{70} - 6 q^{71} - 34 q^{73} + 21 q^{74} + 142 q^{76} - 5 q^{77} - 16 q^{79} - 38 q^{80} - 5 q^{82} - 42 q^{83} - 6 q^{85} + 23 q^{86} + 20 q^{88} + 26 q^{89} - 84 q^{91} - 74 q^{92} - 26 q^{94} - 3 q^{95} - 7 q^{97} - 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2169, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2169, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2169, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(241, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(723, [\chi])\)\(^{\oplus 2}\)