Properties

Label 2169.2.bb
Level $2169$
Weight $2$
Character orbit 2169.bb
Rep. character $\chi_{2169}(154,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $400$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 241 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 984 408 576
Cusp forms 952 400 552
Eisenstein series 32 8 24

Trace form

\( 400 q + 8 q^{2} + 388 q^{4} + q^{5} - 5 q^{7} + 24 q^{8} + O(q^{10}) \) \( 400 q + 8 q^{2} + 388 q^{4} + q^{5} - 5 q^{7} + 24 q^{8} - 7 q^{10} - 20 q^{13} - 5 q^{14} + 364 q^{16} - 15 q^{17} + 32 q^{20} + 5 q^{23} - 109 q^{25} + 40 q^{26} - 35 q^{28} + 31 q^{29} + 25 q^{31} + 96 q^{32} + 20 q^{35} - 58 q^{40} + 42 q^{41} - 5 q^{43} - 75 q^{46} + 11 q^{47} + 21 q^{49} - 35 q^{50} - 65 q^{52} - 13 q^{53} + 40 q^{55} + 45 q^{56} - 42 q^{58} + 11 q^{59} + 13 q^{61} - 95 q^{62} + 388 q^{64} + 4 q^{67} - 35 q^{68} + 65 q^{70} + 25 q^{71} - 35 q^{73} - 30 q^{74} - 39 q^{77} - 52 q^{79} + 131 q^{80} - 61 q^{82} + 24 q^{83} - 80 q^{85} + 65 q^{86} - 39 q^{91} - 20 q^{92} + 28 q^{94} - 5 q^{95} + 10 q^{97} + 66 q^{98} + O(q^{100}) \)

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

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