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Properties

Label 1755.2.dw
Level $1755$
Weight $2$
Character orbit 1755.dw
Rep. character $\chi_{1755}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.dw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
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 352 704
Cusp forms 960 320 640
Eisenstein series 96 32 64

Trace form

\( 320 q + 6 q^{2} + 152 q^{4} + 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 320 q + 6 q^{2} + 152 q^{4} + 2 q^{5} - 4 q^{7} - 16 q^{10} - 2 q^{13} + 48 q^{14} - 132 q^{16} + 12 q^{17} - 6 q^{20} + 2 q^{22} + 16 q^{23} - 24 q^{28} - 4 q^{31} - 18 q^{32} - 16 q^{34} + 46 q^{35} - 4 q^{37} - 32 q^{38} - 20 q^{40} - 4 q^{41} - 8 q^{44} - 16 q^{46} + 14 q^{47} + 224 q^{49} + 70 q^{50} + 6 q^{52} + 16 q^{53} - 4 q^{55} - 14 q^{58} + 16 q^{59} - 8 q^{61} + 28 q^{62} - 192 q^{64} + 2 q^{65} + 76 q^{68} - 44 q^{70} + 28 q^{76} + 44 q^{77} - 4 q^{80} + 20 q^{82} - 8 q^{83} + 56 q^{85} + 40 q^{86} - 2 q^{88} - 16 q^{91} + 56 q^{92} + 6 q^{95} + 282 q^{98} + O(q^{100}) \)

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

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