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Properties

Label 1755.2.dz
Level $1755$
Weight $2$
Character orbit 1755.dz
Rep. character $\chi_{1755}(4,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1488$
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.dz (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1755 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1536 1536 0
Cusp forms 1488 1488 0
Eisenstein series 48 48 0

Trace form

\( 1488 q - 6 q^{4} - 18 q^{6} + 6 q^{9} + O(q^{10}) \) \( 1488 q - 6 q^{4} - 18 q^{6} + 6 q^{9} + 3 q^{10} - 18 q^{11} - 24 q^{14} - 9 q^{15} - 18 q^{16} - 18 q^{19} - 9 q^{20} + 36 q^{24} - 12 q^{25} - 24 q^{26} - 6 q^{29} - 39 q^{30} + 36 q^{34} + 3 q^{35} - 6 q^{36} - 66 q^{39} + 6 q^{40} + 18 q^{41} - 72 q^{44} - 54 q^{45} - 18 q^{46} - 6 q^{49} - 9 q^{50} - 18 q^{51} - 18 q^{54} - 6 q^{55} + 102 q^{56} - 18 q^{59} + 54 q^{60} - 6 q^{61} - 672 q^{64} - 27 q^{65} + 72 q^{66} - 18 q^{69} - 81 q^{70} - 6 q^{74} - 51 q^{75} - 18 q^{76} - 60 q^{79} + 54 q^{80} + 174 q^{81} + 54 q^{84} + 36 q^{85} + 162 q^{86} - 69 q^{90} - 6 q^{91} - 6 q^{94} - 33 q^{95} - 144 q^{96} - 180 q^{99} + O(q^{100}) \)

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.