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Properties

Label 2169.2.dt
Level $2169$
Weight $2$
Character orbit 2169.dt
Rep. character $\chi_{2169}(35,\cdot)$
Character field $\Q(\zeta_{240})$
Dimension $5120$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.dt (of order \(240\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 723 \)
Character field: \(\Q(\zeta_{240})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 15744 5120 10624
Cusp forms 15232 5120 10112
Eisenstein series 512 0 512

Trace form

\( 5120 q + 64 q^{4} + O(q^{10}) \) \( 5120 q + 64 q^{4} - 96 q^{16} - 64 q^{19} + 96 q^{22} + 96 q^{25} + 224 q^{28} + 192 q^{31} - 16 q^{34} - 48 q^{40} + 64 q^{46} + 192 q^{49} - 144 q^{52} + 32 q^{55} - 128 q^{61} + 288 q^{64} - 32 q^{70} + 112 q^{73} - 192 q^{76} - 64 q^{79} + 96 q^{85} + 192 q^{88} - 288 q^{91} - 64 q^{94} - 416 q^{97} + O(q^{100}) \)

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

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