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Properties

Label 1755.2.fa
Level $1755$
Weight $2$
Character orbit 1755.fa
Rep. character $\chi_{1755}(59,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2976$
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.fa (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1755 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 3072 3072 0
Cusp forms 2976 2976 0
Eisenstein series 96 96 0

Trace form

\( 2976 q - 36 q^{4} - 12 q^{5} - 24 q^{6} - 12 q^{9} + O(q^{10}) \) \( 2976 q - 36 q^{4} - 12 q^{5} - 24 q^{6} - 12 q^{9} - 18 q^{10} - 48 q^{11} - 48 q^{14} - 60 q^{15} - 12 q^{16} - 12 q^{19} - 24 q^{21} - 96 q^{24} - 12 q^{29} - 18 q^{30} - 24 q^{31} + 24 q^{34} - 18 q^{35} - 36 q^{36} + 24 q^{39} - 48 q^{41} - 36 q^{44} - 108 q^{45} - 12 q^{46} - 36 q^{49} + 90 q^{50} + 180 q^{51} - 96 q^{54} - 12 q^{55} - 36 q^{56} - 24 q^{59} - 126 q^{60} - 12 q^{61} - 126 q^{65} - 48 q^{66} - 36 q^{69} + 42 q^{70} - 36 q^{71} + 36 q^{74} - 18 q^{75} - 72 q^{76} - 120 q^{79} + 144 q^{80} + 12 q^{81} + 300 q^{84} + 48 q^{85} + 84 q^{86} - 36 q^{89} - 162 q^{90} - 12 q^{91} - 12 q^{94} - 18 q^{95} - 420 q^{96} - 252 q^{99} + O(q^{100}) \)

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.