Properties

Label 1089.3.be
Level $1089$
Weight $3$
Character orbit 1089.be
Rep. character $\chi_{1089}(7,\cdot)$
Character field $\Q(\zeta_{330})$
Dimension $20960$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1089.be (of order \(330\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{330})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 21280 21280 0
Cusp forms 20960 20960 0
Eisenstein series 320 320 0

Trace form

\( 20960 q - 39 q^{2} - 56 q^{3} + 479 q^{4} - 41 q^{5} - 102 q^{6} - 39 q^{7} - 156 q^{8} - 84 q^{9} + O(q^{10}) \) \( 20960 q - 39 q^{2} - 56 q^{3} + 479 q^{4} - 41 q^{5} - 102 q^{6} - 39 q^{7} - 156 q^{8} - 84 q^{9} - 176 q^{10} - 40 q^{11} - 377 q^{12} - 39 q^{13} - 57 q^{14} - 303 q^{15} - 1057 q^{16} - 156 q^{17} - 42 q^{18} - 96 q^{19} + 11 q^{20} - 187 q^{21} - 60 q^{22} - 54 q^{23} + 132 q^{24} - 1311 q^{25} - 132 q^{26} + 13 q^{27} - 156 q^{28} - 84 q^{29} + 90 q^{30} - 41 q^{31} - 44 q^{32} + 7 q^{33} + 20 q^{34} - 306 q^{35} - 118 q^{36} - 164 q^{37} + 447 q^{38} - 602 q^{39} - 130 q^{40} - 309 q^{41} - 246 q^{42} - 44 q^{43} - 742 q^{44} - 99 q^{45} - 196 q^{46} - 149 q^{47} + 367 q^{48} + 1709 q^{49} - 164 q^{50} + 882 q^{51} - 39 q^{52} + 820 q^{53} + 176 q^{54} - 86 q^{55} + 50 q^{56} + 90 q^{57} - 129 q^{58} - 137 q^{59} - 350 q^{60} - 39 q^{61} + 294 q^{62} + 263 q^{63} - 4044 q^{64} - 44 q^{65} - 390 q^{66} - 120 q^{67} + 116 q^{68} - 532 q^{69} + 16 q^{70} - 68 q^{71} + 1045 q^{72} - 156 q^{73} - 1299 q^{74} - 79 q^{75} + 352 q^{76} - 453 q^{77} - 394 q^{78} - 39 q^{79} - 6276 q^{80} - 1028 q^{81} + 108 q^{82} - 444 q^{83} - 1645 q^{84} + 291 q^{85} + 199 q^{86} - 187 q^{87} - 708 q^{88} + 834 q^{89} - 2246 q^{90} + 816 q^{91} - 1023 q^{92} - 963 q^{93} - 50 q^{94} + 105 q^{95} + 1098 q^{96} + 229 q^{97} - 2288 q^{98} - 1044 q^{99} + O(q^{100}) \)

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

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