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Properties

Label 1764.3.ct
Level $1764$
Weight $3$
Character orbit 1764.ct
Rep. character $\chi_{1764}(151,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.ct (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1764 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 8112 8112 0
Cusp forms 8016 8016 0
Eisenstein series 96 96 0

Trace form

\( 8016 q - 5 q^{2} - 5 q^{4} - 16 q^{5} - 14 q^{6} - 20 q^{8} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 5 q^{2} - 5 q^{4} - 16 q^{5} - 14 q^{6} - 20 q^{8} - 26 q^{9} - 18 q^{10} - 114 q^{12} - 10 q^{13} - 112 q^{14} - 5 q^{16} - 52 q^{17} - 15 q^{18} + 27 q^{20} + 2 q^{21} - 13 q^{22} + 48 q^{24} + 3244 q^{25} - 30 q^{26} - 40 q^{28} + 302 q^{29} - 42 q^{30} - 185 q^{32} + 10 q^{33} - 9 q^{34} - 14 q^{36} - 52 q^{37} - 18 q^{38} - 33 q^{40} - 10 q^{41} - 130 q^{42} - 25 q^{44} - 166 q^{45} - 34 q^{46} - 3 q^{48} - 12 q^{49} - 29 q^{50} + 24 q^{52} - 52 q^{53} - 55 q^{54} + 1109 q^{56} - 110 q^{57} + 289 q^{60} - 10 q^{61} + 396 q^{62} - 20 q^{64} - 210 q^{65} - 874 q^{66} + 113 q^{68} - 230 q^{69} + 38 q^{70} - 70 q^{72} - 52 q^{73} - 252 q^{74} - 213 q^{76} + 232 q^{77} + 1603 q^{78} + 95 q^{80} + 174 q^{81} - 30 q^{82} - 2291 q^{84} - 60 q^{85} - 70 q^{86} + 56 q^{88} + 68 q^{89} + 82 q^{90} - 1987 q^{92} + 74 q^{93} - 37 q^{94} - 412 q^{96} - 24 q^{97} + 43 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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