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Properties

Label 1089.3.x
Level $1089$
Weight $3$
Character orbit 1089.x
Rep. character $\chi_{1089}(43,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $5240$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1089.x (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1089, [\chi])\).

Total New Old
Modular forms 5320 5320 0
Cusp forms 5240 5240 0
Eisenstein series 80 80 0

Trace form

\( 5240 q - 11 q^{2} - 44 q^{3} - 529 q^{4} - 9 q^{5} + 22 q^{6} - 11 q^{7} - 44 q^{8} - 36 q^{9} + O(q^{10}) \) \( 5240 q - 11 q^{2} - 44 q^{3} - 529 q^{4} - 9 q^{5} + 22 q^{6} - 11 q^{7} - 44 q^{8} - 36 q^{9} - 44 q^{10} - 10 q^{11} + 287 q^{12} - 11 q^{13} + 7 q^{14} + 153 q^{15} + 1007 q^{16} - 44 q^{17} + 22 q^{18} - 44 q^{19} - 81 q^{20} + 77 q^{21} + 10 q^{22} + 9 q^{23} - 132 q^{24} + 1261 q^{25} + 172 q^{26} - 38 q^{27} - 44 q^{28} - 11 q^{29} - 220 q^{30} - 9 q^{31} - 11 q^{32} + 18 q^{33} - 65 q^{34} - 44 q^{35} + 158 q^{36} - 36 q^{37} - 317 q^{38} + 77 q^{39} - 11 q^{41} + 21 q^{42} - 11 q^{43} + 182 q^{44} + 9 q^{45} - 44 q^{46} + 99 q^{47} + 3 q^{48} - 1759 q^{49} - 11 q^{50} - 1232 q^{51} - 11 q^{52} - 540 q^{53} - 286 q^{54} - 114 q^{55} - 95 q^{56} + 550 q^{57} - 41 q^{58} - 123 q^{59} + 115 q^{60} - 11 q^{61} - 44 q^{62} - 88 q^{63} + 3884 q^{64} - 11 q^{65} + 625 q^{66} + 75 q^{67} - 11 q^{68} - 123 q^{69} - 311 q^{70} - 612 q^{71} - 1430 q^{72} - 44 q^{73} - 11 q^{74} - 331 q^{75} - 407 q^{76} + 883 q^{77} + 304 q^{78} - 11 q^{79} + 3596 q^{80} + 68 q^{81} + 172 q^{82} - 11 q^{83} - 220 q^{84} - 341 q^{85} - 629 q^{86} + 77 q^{87} + 598 q^{88} - 1014 q^{89} - 44 q^{90} - 596 q^{91} + 453 q^{92} + 838 q^{93} - 275 q^{95} + 77 q^{96} + 171 q^{97} + 2068 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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