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Properties

Label 1323.4.cf
Level $1323$
Weight $4$
Character orbit 1323.cf
Rep. character $\chi_{1323}(47,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $18072$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.cf (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{126})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

Total New Old
Modular forms 18216 18216 0
Cusp forms 18072 18072 0
Eisenstein series 144 144 0

Trace form

\( 18072 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} - 174 q^{6} - 36 q^{7} - 45 q^{8} - 39 q^{9} + O(q^{10}) \) \( 18072 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} - 174 q^{6} - 36 q^{7} - 45 q^{8} - 39 q^{9} - 12 q^{10} - 39 q^{11} - 33 q^{12} - 42 q^{13} + 996 q^{14} - 30 q^{15} + 9 q^{16} - 54 q^{17} - 18 q^{18} - 54 q^{19} + 30 q^{20} - 12 q^{21} - 30 q^{22} + 969 q^{23} + 210 q^{24} - 39 q^{25} - 42 q^{27} - 72 q^{28} - 1038 q^{29} + 396 q^{30} - 54 q^{31} - 231 q^{32} - 33 q^{33} - 114 q^{34} - 54 q^{35} - 5532 q^{36} - 15 q^{37} - 201 q^{38} - 459 q^{39} - 33 q^{40} - 42 q^{41} - 9795 q^{42} - 30 q^{43} - 63 q^{44} + 2937 q^{45} - 15 q^{46} - 825 q^{47} + 1152 q^{49} - 783 q^{50} - 1461 q^{51} - 33 q^{52} + 7560 q^{53} + 6645 q^{54} - 84 q^{55} + 1179 q^{56} + 7386 q^{57} - 39 q^{58} - 33 q^{59} - 759 q^{60} + 129 q^{61} - 1944 q^{62} + 1962 q^{63} - 93711 q^{64} - 1215 q^{65} + 3567 q^{66} - 18 q^{67} - 3663 q^{68} + 25698 q^{69} + 477 q^{70} - 45 q^{71} + 1353 q^{72} - 21 q^{73} - 2463 q^{74} + 30459 q^{75} - 810 q^{76} + 2004 q^{77} - 192 q^{78} - 18 q^{79} + 4608 q^{80} - 39 q^{81} - 66 q^{82} - 5532 q^{83} - 10566 q^{84} + 345 q^{85} + 4119 q^{86} - 33 q^{87} - 1671 q^{88} - 54 q^{89} + 6519 q^{90} + 522 q^{91} + 21960 q^{92} + 13821 q^{93} - 33 q^{94} - 3678 q^{95} + 35499 q^{96} - 2961 q^{98} - 11664 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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