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Properties

Label 1755.2.bf
Level $1755$
Weight $2$
Character orbit 1755.bf
Rep. character $\chi_{1755}(244,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 528 224 304
Cusp forms 480 224 256
Eisenstein series 48 0 48

Trace form

\( 224 q - 112 q^{4} + O(q^{10}) \) \( 224 q - 112 q^{4} - 12 q^{10} - 120 q^{16} - 12 q^{19} - 20 q^{25} + 76 q^{40} + 48 q^{46} - 104 q^{49} - 12 q^{55} - 52 q^{61} + 208 q^{64} + 48 q^{76} + 32 q^{79} - 6 q^{85} + 28 q^{91} - 84 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)