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Properties

Label 1764.2.cm
Level $1764$
Weight $2$
Character orbit 1764.cm
Rep. character $\chi_{1764}(11,\cdot)$
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.cm (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

\( 3984 q - 21 q^{2} - 5 q^{4} - 36 q^{5} - 8 q^{6} - 26 q^{9} + O(q^{10}) \) \( 3984 q - 21 q^{2} - 5 q^{4} - 36 q^{5} - 8 q^{6} - 26 q^{9} - 30 q^{10} - 90 q^{12} - 10 q^{13} - 108 q^{14} - 5 q^{16} - 9 q^{18} - 15 q^{20} - 22 q^{21} - q^{22} - 332 q^{25} - 6 q^{26} - 28 q^{28} - 18 q^{29} + 12 q^{30} - 21 q^{32} - 38 q^{33} - 3 q^{34} - 26 q^{36} - 52 q^{37} - 18 q^{38} - 3 q^{40} - 30 q^{41} + 32 q^{42} - 57 q^{44} - 10 q^{45} - 22 q^{46} + 15 q^{48} - 12 q^{49} - 51 q^{50} - 37 q^{54} + 3 q^{56} - 50 q^{57} - 12 q^{58} - 83 q^{60} - 10 q^{61} + 42 q^{62} - 20 q^{64} - 42 q^{65} + 164 q^{66} - 9 q^{68} + 34 q^{69} + 20 q^{70} - 10 q^{72} - 52 q^{73} - 30 q^{74} - 57 q^{76} - 12 q^{77} + 85 q^{78} + 87 q^{80} - 126 q^{81} - 24 q^{82} - 113 q^{84} - 72 q^{86} - 16 q^{88} + 60 q^{89} + 148 q^{90} - 45 q^{92} + 26 q^{93} + 11 q^{94} + 8 q^{96} - 24 q^{97} - 57 q^{98} + O(q^{100}) \)

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.