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Properties

Label 1764.2.cz
Level $1764$
Weight $2$
Character orbit 1764.cz
Rep. character $\chi_{1764}(95,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3984$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1764 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

Total New Old
Modular forms 4080 4080 0
Cusp forms 3984 3984 0
Eisenstein series 96 96 0

Trace form

\( 3984 q - 18 q^{2} - 8 q^{4} - 42 q^{5} - 8 q^{6} - 26 q^{9} + O(q^{10}) \) \( 3984 q - 18 q^{2} - 8 q^{4} - 42 q^{5} - 8 q^{6} - 26 q^{9} - 30 q^{10} + 18 q^{12} - 10 q^{13} - 18 q^{14} - 8 q^{16} - 12 q^{18} - 15 q^{20} - 28 q^{21} - q^{22} + 622 q^{25} + 6 q^{26} - 28 q^{28} - 102 q^{29} - 9 q^{30} - 18 q^{32} - 2 q^{33} - 3 q^{34} - 26 q^{36} - 52 q^{37} - 21 q^{38} - 15 q^{40} - 30 q^{41} - q^{42} + 57 q^{44} - 70 q^{45} - 22 q^{46} + 15 q^{48} - 12 q^{49} - 51 q^{50} - 21 q^{52} + 8 q^{54} + 45 q^{56} - 50 q^{57} + 3 q^{58} + 160 q^{60} - 16 q^{61} - 42 q^{62} - 20 q^{64} - 36 q^{65} - 187 q^{66} + 34 q^{69} - 37 q^{70} - 43 q^{72} - 52 q^{73} - 21 q^{74} + 27 q^{76} - 12 q^{77} - 125 q^{78} - 87 q^{80} + 234 q^{81} - 24 q^{82} - 161 q^{84} - 21 q^{86} + 11 q^{88} - 60 q^{89} + 43 q^{90} + 165 q^{92} - 40 q^{93} - 16 q^{94} - q^{96} - 24 q^{97} + 57 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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