Properties

Label 1755.2.bt
Level $1755$
Weight $2$
Character orbit 1755.bt
Rep. character $\chi_{1755}(181,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
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 528 112 416
Cusp forms 480 112 368
Eisenstein series 48 0 48

Trace form

\( 112 q + 56 q^{4} + O(q^{10}) \) \( 112 q + 56 q^{4} + 2 q^{13} - 56 q^{16} - 32 q^{17} + 24 q^{23} + 56 q^{25} - 24 q^{26} + 20 q^{29} + 32 q^{35} + 44 q^{38} - 16 q^{43} + 52 q^{49} + 10 q^{52} + 80 q^{53} - 40 q^{56} + 28 q^{61} - 88 q^{62} - 184 q^{64} + 2 q^{65} + 4 q^{68} - 40 q^{74} - 16 q^{77} + 16 q^{79} + 72 q^{82} - 180 q^{92} - 36 q^{94} + 40 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)