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Properties

Label 1755.2.dg
Level $1755$
Weight $2$
Character orbit 1755.dg
Rep. character $\chi_{1755}(206,\cdot)$
Character field $\Q(\zeta_{12})$
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.dg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1056 224 832
Cusp forms 960 224 736
Eisenstein series 96 0 96

Trace form

\( 224 q - 8 q^{7} - 36 q^{8} + O(q^{10}) \) \( 224 q - 8 q^{7} - 36 q^{8} + 12 q^{11} + 112 q^{16} - 8 q^{19} + 48 q^{26} - 16 q^{28} - 16 q^{31} + 72 q^{32} - 4 q^{37} + 24 q^{41} + 72 q^{47} - 4 q^{52} + 36 q^{58} + 72 q^{59} - 36 q^{62} + 28 q^{67} + 48 q^{71} + 28 q^{73} + 16 q^{76} - 144 q^{77} - 12 q^{79} + 48 q^{80} + 36 q^{83} - 12 q^{85} + 108 q^{86} - 60 q^{89} + 16 q^{91} + 120 q^{92} - 4 q^{97} - 96 q^{98} + O(q^{100}) \)

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

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