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Properties

Label 1755.2.bm
Level $1755$
Weight $2$
Character orbit 1755.bm
Rep. character $\chi_{1755}(316,\cdot)$
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.bm (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

\( 112 q + 56 q^{4} + O(q^{10}) \) \( 112 q + 56 q^{4} + 2 q^{13} - 56 q^{16} + 16 q^{17} + 6 q^{19} - 48 q^{23} + 56 q^{25} + 12 q^{26} - 10 q^{29} - 24 q^{31} - 36 q^{32} - 16 q^{35} - 6 q^{37} + 44 q^{38} - 16 q^{43} - 36 q^{47} - 104 q^{49} + 34 q^{52} + 32 q^{53} + 80 q^{56} - 24 q^{59} + 28 q^{61} + 26 q^{62} - 76 q^{64} - 4 q^{65} + 148 q^{68} + 24 q^{71} - 16 q^{74} + 56 q^{77} - 8 q^{79} + 18 q^{82} - 18 q^{83} + 18 q^{85} - 6 q^{86} + 36 q^{89} - 12 q^{92} + 72 q^{94} + 28 q^{95} - 48 q^{98} + O(q^{100}) \)

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

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