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Properties

Label 2169.2.i
Level $2169$
Weight $2$
Character orbit 2169.i
Rep. character $\chi_{2169}(64,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $484$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 492 204 288
Cusp forms 476 200 276
Eisenstein series 16 4 12

Trace form

\( 200 q - 196 q^{4} + O(q^{10}) \) \( 200 q - 196 q^{4} + 4 q^{10} + 4 q^{11} - 4 q^{13} + 8 q^{14} + 196 q^{16} - 8 q^{17} + 8 q^{19} + 26 q^{22} + 10 q^{23} - 160 q^{25} - 10 q^{26} - 2 q^{28} + 6 q^{31} + 6 q^{34} - 14 q^{35} - 18 q^{37} - 26 q^{38} - 20 q^{40} - 8 q^{43} - 14 q^{44} + 10 q^{46} - 28 q^{52} - 18 q^{55} - 62 q^{56} - 60 q^{58} - 64 q^{62} - 188 q^{64} + 48 q^{65} - 32 q^{68} - 36 q^{70} + 8 q^{71} + 24 q^{73} - 6 q^{74} - 64 q^{76} - 24 q^{82} + 16 q^{83} - 42 q^{85} - 86 q^{86} - 10 q^{88} + 18 q^{89} + 36 q^{91} + 30 q^{92} - 28 q^{94} + 12 q^{95} + 24 q^{97} - 12 q^{98} + O(q^{100}) \)

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

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