Properties

Label 2169.2.cn
Level $2169$
Weight $2$
Character orbit 2169.cn
Rep. character $\chi_{2169}(289,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $1616$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.cn (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 3936 1648 2288
Cusp forms 3808 1616 2192
Eisenstein series 128 32 96

Trace form

\( 1616 q + 16 q^{2} + 16 q^{5} - 8 q^{7} - 16 q^{8} + O(q^{10}) \) \( 1616 q + 16 q^{2} + 16 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{10} + 16 q^{11} - 16 q^{13} + 76 q^{14} - 1760 q^{16} - 48 q^{17} - 36 q^{19} - 56 q^{20} - 40 q^{22} + 32 q^{23} - 20 q^{25} + 44 q^{26} + 16 q^{28} + 36 q^{29} - 56 q^{31} - 36 q^{32} - 4 q^{34} + 48 q^{35} - 20 q^{37} + 12 q^{38} + 60 q^{40} + 12 q^{41} - 4 q^{43} - 32 q^{44} - 48 q^{46} + 8 q^{47} - 76 q^{49} - 356 q^{50} + 40 q^{52} + 28 q^{53} + 12 q^{55} - 20 q^{56} + 52 q^{58} - 12 q^{59} - 48 q^{61} - 116 q^{62} + 28 q^{65} - 12 q^{67} + 4 q^{68} + 4 q^{70} + 24 q^{71} + 36 q^{73} + 208 q^{74} + 12 q^{76} + 176 q^{77} - 24 q^{79} + 180 q^{80} - 140 q^{82} + 20 q^{83} - 48 q^{85} + 68 q^{86} - 52 q^{88} + 44 q^{89} + 76 q^{91} - 140 q^{92} - 28 q^{94} - 64 q^{95} + 100 q^{97} + 56 q^{98} + O(q^{100}) \)

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

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