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Properties

Label 1764.3.cs
Level $1764$
Weight $3$
Character orbit 1764.cs
Rep. character $\chi_{1764}(43,\cdot)$
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.cs (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

\( 8016 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 2 q^{6} - 20 q^{8} - 20 q^{9} + O(q^{10}) \) \( 8016 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 2 q^{6} - 20 q^{8} - 20 q^{9} - 36 q^{10} + 33 q^{12} - 10 q^{13} - 88 q^{14} - 5 q^{16} - 40 q^{17} + 18 q^{18} - 69 q^{20} + 2 q^{21} + 11 q^{22} - 186 q^{24} + 3250 q^{25} - 36 q^{26} + 8 q^{28} - 130 q^{29} - 102 q^{30} - 185 q^{32} + 16 q^{33} + 3 q^{34} - 2 q^{36} - 40 q^{37} + 75 q^{38} + 45 q^{40} - 10 q^{41} + 200 q^{42} + 176 q^{44} - 280 q^{45} - 4 q^{46} + 354 q^{48} - 12 q^{49} + 22 q^{50} - 69 q^{52} - 40 q^{53} - 82 q^{54} + 983 q^{56} + 160 q^{57} - 21 q^{58} + 340 q^{60} - 10 q^{61} - 852 q^{62} - 20 q^{64} - 210 q^{65} + 1112 q^{66} - 130 q^{68} + 64 q^{69} - 109 q^{70} + 488 q^{72} - 40 q^{73} + 507 q^{74} + 75 q^{76} + 232 q^{77} - 722 q^{78} + 80 q^{80} + 180 q^{81} - 36 q^{82} - 1472 q^{84} + 90 q^{85} + 119 q^{86} - 133 q^{88} + 440 q^{89} + 1276 q^{90} + 809 q^{92} + 50 q^{93} + 11 q^{94} + 989 q^{96} - 24 q^{97} - 1148 q^{98} + O(q^{100}) \)

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.