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Properties

Label 2169.2.x
Level $2169$
Weight $2$
Character orbit 2169.x
Rep. character $\chi_{2169}(271,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $404$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 984 412 572
Cusp forms 952 404 548
Eisenstein series 32 8 24

Trace form

\( 404 q + 4 q^{2} + 4 q^{5} - 12 q^{7} - 4 q^{8} + O(q^{10}) \) \( 404 q + 4 q^{2} + 4 q^{5} - 12 q^{7} - 4 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} - 16 q^{14} - 420 q^{16} + 8 q^{17} + 16 q^{19} - 4 q^{20} + 20 q^{22} - 12 q^{23} - 24 q^{26} + 44 q^{28} - 16 q^{29} - 4 q^{31} + 16 q^{32} - 16 q^{34} + 12 q^{35} + 8 q^{38} + 8 q^{41} - 16 q^{43} - 28 q^{44} - 52 q^{46} + 12 q^{47} - 64 q^{49} + 16 q^{50} + 20 q^{52} - 8 q^{53} - 32 q^{55} - 40 q^{56} - 72 q^{58} + 32 q^{59} - 12 q^{61} + 36 q^{62} + 32 q^{65} - 8 q^{67} - 64 q^{68} - 24 q^{70} - 4 q^{71} + 4 q^{73} + 32 q^{74} + 28 q^{76} + 84 q^{77} + 44 q^{79} + 20 q^{80} + 28 q^{85} - 48 q^{86} + 112 q^{88} - 24 q^{89} + 24 q^{91} - 40 q^{92} + 8 q^{94} - 76 q^{95} - 116 q^{98} + O(q^{100}) \)

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

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