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Properties

Label 2169.2.bv
Level $2169$
Weight $2$
Character orbit 2169.bv
Rep. character $\chi_{2169}(361,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $800$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.bv (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 1968 816 1152
Cusp forms 1904 800 1104
Eisenstein series 64 16 48

Trace form

\( 800 q + 8 q^{2} + 12 q^{4} + 8 q^{5} - 24 q^{7} + 16 q^{8} + O(q^{10}) \) \( 800 q + 8 q^{2} + 12 q^{4} + 8 q^{5} - 24 q^{7} + 16 q^{8} + 4 q^{10} + 8 q^{11} - 8 q^{13} - 32 q^{14} + 392 q^{16} + 40 q^{17} - 28 q^{19} + 16 q^{20} - 32 q^{22} - 12 q^{23} + 36 q^{26} + 32 q^{28} + 16 q^{29} - 64 q^{31} + 56 q^{32} + 4 q^{34} + 24 q^{35} - 12 q^{37} + 4 q^{38} + 28 q^{41} - 24 q^{43} - 44 q^{44} - 56 q^{46} + 24 q^{47} + 132 q^{49} - 184 q^{50} - 136 q^{52} - 16 q^{53} + 20 q^{55} - 32 q^{56} - 24 q^{58} - 20 q^{59} + 48 q^{62} + 100 q^{65} - 28 q^{67} - 8 q^{68} + 12 q^{70} + 16 q^{71} - 120 q^{73} - 20 q^{74} + 72 q^{76} - 72 q^{77} - 56 q^{79} + 64 q^{80} + 96 q^{82} + 96 q^{83} - 4 q^{85} - 36 q^{86} - 4 q^{88} + 48 q^{89} + 40 q^{91} + 172 q^{92} - 20 q^{94} - 104 q^{95} - 48 q^{97} + 32 q^{98} + O(q^{100}) \)

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

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