Properties

Label 1755.2.eu
Level $1755$
Weight $2$
Character orbit 1755.eu
Rep. character $\chi_{1755}(187,\cdot)$
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.eu (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

\( 2976 q - 24 q^{2} - 24 q^{3} - 12 q^{5} - 24 q^{6} - 12 q^{8} + O(q^{10}) \) \( 2976 q - 24 q^{2} - 24 q^{3} - 12 q^{5} - 24 q^{6} - 12 q^{8} - 36 q^{11} - 12 q^{13} + 12 q^{15} - 48 q^{16} - 24 q^{21} - 24 q^{22} - 48 q^{23} + 36 q^{24} - 48 q^{26} - 24 q^{27} - 24 q^{31} + 24 q^{32} - 24 q^{33} + 24 q^{34} - 12 q^{35} + 24 q^{38} + 24 q^{40} - 48 q^{41} - 24 q^{42} - 48 q^{44} - 54 q^{45} - 12 q^{46} - 24 q^{48} - 192 q^{50} - 36 q^{52} - 48 q^{53} - 48 q^{55} - 60 q^{57} + 108 q^{60} - 48 q^{61} + 60 q^{63} - 1320 q^{64} - 12 q^{65} - 48 q^{66} - 24 q^{67} + 24 q^{68} + 96 q^{69} - 42 q^{70} - 12 q^{71} - 12 q^{73} + 24 q^{76} + 96 q^{77} - 150 q^{78} + 72 q^{80} + 24 q^{81} + 120 q^{84} + 18 q^{85} + 84 q^{86} - 120 q^{87} + 120 q^{88} - 120 q^{90} - 12 q^{91} + 264 q^{92} - 228 q^{96} - 24 q^{97} + 216 q^{98} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.