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Properties

Label 1755.2.fg
Level $1755$
Weight $2$
Character orbit 1755.fg
Rep. character $\chi_{1755}(68,\cdot)$
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.fg (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

\( 2976 q - 6 q^{2} - 6 q^{3} - 24 q^{5} - 12 q^{6} - 6 q^{7} - 36 q^{8} + O(q^{10}) \) \( 2976 q - 6 q^{2} - 6 q^{3} - 24 q^{5} - 12 q^{6} - 6 q^{7} - 36 q^{8} - 12 q^{10} - 36 q^{11} - 24 q^{12} - 12 q^{13} - 6 q^{15} - 12 q^{16} - 18 q^{17} - 24 q^{18} - 6 q^{20} - 48 q^{21} - 6 q^{22} - 54 q^{23} - 24 q^{25} - 24 q^{27} - 12 q^{28} - 42 q^{30} - 48 q^{31} - 30 q^{32} - 6 q^{33} - 12 q^{36} - 12 q^{37} - 48 q^{38} + 36 q^{41} - 6 q^{42} - 6 q^{43} + 54 q^{45} - 24 q^{46} - 54 q^{47} + 30 q^{48} - 6 q^{50} - 72 q^{51} - 24 q^{52} - 12 q^{55} - 12 q^{56} - 6 q^{57} - 6 q^{58} - 60 q^{60} - 12 q^{61} - 18 q^{62} - 90 q^{63} + 132 q^{65} + 144 q^{66} - 6 q^{67} + 42 q^{68} - 24 q^{70} - 36 q^{71} + 18 q^{72} - 12 q^{73} - 78 q^{75} + 180 q^{76} + 72 q^{77} + 24 q^{78} - 96 q^{81} - 12 q^{82} + 96 q^{83} - 6 q^{85} - 156 q^{86} - 54 q^{87} - 114 q^{88} + 30 q^{90} - 12 q^{91} - 180 q^{92} - 6 q^{93} + 24 q^{95} + 264 q^{96} - 6 q^{97} + 324 q^{98} + O(q^{100}) \)

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.