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Properties

Label 2169.2.dc
Level $2169$
Weight $2$
Character orbit 2169.dc
Rep. character $\chi_{2169}(82,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1584$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.dc (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 3936 1616 2320
Cusp forms 3808 1584 2224
Eisenstein series 128 32 96

Trace form

\( 1584 q + 24 q^{2} + 756 q^{4} + 20 q^{5} - 30 q^{7} + O(q^{10}) \) \( 1584 q + 24 q^{2} + 756 q^{4} + 20 q^{5} - 30 q^{7} - 48 q^{10} + 24 q^{11} - 10 q^{13} + 32 q^{14} - 708 q^{16} + 46 q^{17} - 40 q^{19} + 18 q^{20} - 26 q^{22} + 6 q^{23} + 392 q^{25} + 24 q^{26} - 40 q^{28} + 38 q^{29} + 56 q^{31} - 42 q^{32} + 68 q^{34} - 40 q^{35} - 42 q^{37} + 18 q^{38} - 4 q^{40} + 20 q^{41} - 36 q^{43} + 22 q^{44} - 76 q^{46} + 20 q^{47} - 2 q^{49} + 254 q^{50} + 18 q^{52} - 10 q^{53} - 10 q^{55} - 124 q^{56} - 44 q^{58} + 36 q^{59} + 80 q^{61} + 36 q^{62} - 1176 q^{64} + 60 q^{65} - 44 q^{67} - 8 q^{68} + 16 q^{71} - 32 q^{73} + 90 q^{74} + 104 q^{76} + 70 q^{77} - 40 q^{79} - 328 q^{80} + 44 q^{82} + 16 q^{83} - 32 q^{85} - 40 q^{86} + 288 q^{88} + 60 q^{89} + 12 q^{91} + 70 q^{92} - 274 q^{94} + 198 q^{95} + 136 q^{97} - 52 q^{98} + O(q^{100}) \)

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

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