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Properties

Label 1755.2.be
Level $1755$
Weight $2$
Character orbit 1755.be
Rep. character $\chi_{1755}(64,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
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 528 176 352
Cusp forms 480 160 320
Eisenstein series 48 16 32

Trace form

\( 160 q - 80 q^{4} + O(q^{10}) \) \( 160 q - 80 q^{4} + 4 q^{14} - 80 q^{16} - 2 q^{25} - 16 q^{26} + 36 q^{29} - 4 q^{35} - 12 q^{40} - 60 q^{49} - 28 q^{55} + 56 q^{56} - 4 q^{61} + 136 q^{64} - 44 q^{65} + 44 q^{74} + 8 q^{79} + 8 q^{91} + 36 q^{94} + 24 q^{95} + O(q^{100}) \)

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

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