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Properties

Label 2169.2.df
Level $2169$
Weight $2$
Character orbit 2169.df
Rep. character $\chi_{2169}(17,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $2624$
Sturm bound $484$

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Defining parameters

Level: \( N \) \(=\) \( 2169 = 3^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2169.df (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 723 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(484\)

Dimensions

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

Total New Old
Modular forms 7872 2624 5248
Cusp forms 7616 2624 4992
Eisenstein series 256 0 256

Trace form

\( 2624 q + 32 q^{4} + O(q^{10}) \) \( 2624 q + 32 q^{4} + 64 q^{19} - 96 q^{22} - 96 q^{25} - 160 q^{31} + 16 q^{34} + 48 q^{40} - 64 q^{46} + 96 q^{49} + 208 q^{52} - 32 q^{55} + 128 q^{61} - 192 q^{64} + 32 q^{70} - 128 q^{73} - 256 q^{76} + 64 q^{79} + 48 q^{85} - 192 q^{88} + 288 q^{91} + 64 q^{94} + 368 q^{97} + O(q^{100}) \)

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

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