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Properties

Label 1764.3.ca
Level $1764$
Weight $3$
Character orbit 1764.ca
Rep. character $\chi_{1764}(47,\cdot)$
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.ca (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

\( 8016 q - 18 q^{2} - 8 q^{4} - 30 q^{5} - 26 q^{6} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 18 q^{2} - 8 q^{4} - 30 q^{5} - 26 q^{6} - 26 q^{9} - 22 q^{10} + 24 q^{12} - 14 q^{13} - 18 q^{14} - 8 q^{16} - 48 q^{18} - 21 q^{20} + 28 q^{21} + 3 q^{22} + 16 q^{24} - 6530 q^{25} + 12 q^{26} - 40 q^{28} - 462 q^{29} - 7 q^{30} - 18 q^{32} - 22 q^{33} + 5 q^{34} + 26 q^{36} - 52 q^{37} - 195 q^{38} - 7 q^{40} - 42 q^{41} + 81 q^{42} + 195 q^{44} + 98 q^{45} - 18 q^{46} + 27 q^{48} - 12 q^{49} + 39 q^{50} - 7 q^{52} + 226 q^{54} + 3 q^{56} + 70 q^{57} + 11 q^{58} + 1020 q^{60} - 8 q^{61} + 60 q^{62} - 20 q^{64} - 36 q^{65} + 2239 q^{66} + 414 q^{68} - 86 q^{69} + 135 q^{70} + 165 q^{72} - 44 q^{73} - 21 q^{74} - 71 q^{76} - 180 q^{77} - 937 q^{78} - 171 q^{80} - 546 q^{81} - 34 q^{82} + 1533 q^{84} - 60 q^{85} - 21 q^{86} + 123 q^{88} + 360 q^{89} - 763 q^{90} - 2715 q^{92} + 224 q^{93} - 4 q^{94} - 961 q^{96} - 141 q^{98} + O(q^{100}) \)

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.