↑

Properties

Label 1764.3.cc
Level $1764$
Weight $3$
Character orbit 1764.cc
Rep. character $\chi_{1764}(319,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $8016$
Sturm bound $1008$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.cc (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

\( 8016 q - 8 q^{2} - 8 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{8} - 26 q^{9} + O(q^{10}) \) \( 8016 q - 8 q^{2} - 8 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{8} - 26 q^{9} - 18 q^{10} + 30 q^{12} - 10 q^{13} + 182 q^{14} - 8 q^{16} - 52 q^{17} + 36 q^{18} + 27 q^{20} - 76 q^{21} - 13 q^{22} + 48 q^{24} - 6530 q^{25} - 30 q^{26} - 40 q^{28} - 202 q^{29} + 45 q^{30} + 82 q^{32} - 98 q^{33} - 9 q^{34} - 14 q^{36} - 52 q^{37} + 15 q^{38} + 45 q^{40} - 10 q^{41} + 35 q^{42} - 25 q^{44} + 134 q^{45} - 34 q^{46} - 3 q^{48} - 12 q^{49} - 29 q^{50} - 69 q^{52} - 52 q^{53} + 224 q^{54} - 2257 q^{56} - 110 q^{57} - 21 q^{58} - 800 q^{60} - 16 q^{61} + 396 q^{62} - 20 q^{64} + 84 q^{65} - 469 q^{66} - 226 q^{68} - 230 q^{69} + 53 q^{70} + 293 q^{72} - 52 q^{73} + 483 q^{74} + 123 q^{76} - 356 q^{77} - 1127 q^{78} + 95 q^{80} - 546 q^{81} - 30 q^{82} - 1475 q^{84} - 60 q^{85} + 119 q^{86} - 133 q^{88} + 68 q^{89} + 607 q^{90} + 1163 q^{92} + 44 q^{93} + 8 q^{94} - 853 q^{96} - 24 q^{97} + 43 q^{98} + O(q^{100}) \)

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.