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Properties

Label 1764.4.cz
Level $1764$
Weight $4$
Character orbit 1764.cz
Rep. character $\chi_{1764}(95,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12048$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1764 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

Total New Old
Modular forms 12144 12144 0
Cusp forms 12048 12048 0
Eisenstein series 96 96 0

Trace form

\( 12048 q - 18 q^{2} - 8 q^{4} - 42 q^{5} - 2 q^{6} - 26 q^{9} + O(q^{10}) \) \( 12048 q - 18 q^{2} - 8 q^{4} - 42 q^{5} - 2 q^{6} - 26 q^{9} - 42 q^{10} - 234 q^{12} - 10 q^{13} - 18 q^{14} - 8 q^{16} - 60 q^{18} - 15 q^{20} - 268 q^{21} + 11 q^{22} + 264 q^{24} + 49390 q^{25} + 24 q^{26} - 88 q^{28} - 534 q^{29} - 93 q^{30} - 18 q^{32} + 190 q^{33} + 3 q^{34} + 754 q^{36} - 52 q^{37} - 21 q^{38} - 255 q^{40} - 30 q^{41} + 299 q^{42} - 771 q^{44} - 1246 q^{45} - 10 q^{46} - 537 q^{48} - 12 q^{49} - 411 q^{50} - 261 q^{52} - 82 q^{54} - 963 q^{56} - 290 q^{57} + 27 q^{58} - 6728 q^{60} - 16 q^{61} - 168 q^{62} - 20 q^{64} - 36 q^{65} - 97 q^{66} - 1550 q^{69} - 865 q^{70} - 1603 q^{72} - 52 q^{73} - 21 q^{74} + 507 q^{76} - 1020 q^{77} - 6305 q^{78} + 3297 q^{80} - 20046 q^{81} - 18 q^{82} - 13121 q^{84} + 240 q^{85} - 21 q^{86} + 1019 q^{88} + 3180 q^{89} - 7541 q^{90} + 23925 q^{92} - 184 q^{93} - 40 q^{94} - 10801 q^{96} - 24 q^{97} - 4515 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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