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Properties

Label 1089.2.bd
Level $1089$
Weight $2$
Character orbit 1089.bd
Rep. character $\chi_{1089}(2,\cdot)$
Character field $\Q(\zeta_{330})$
Dimension $10400$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.bd (of order \(330\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{330})\)
Sturm bound: \(264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1089, [\chi])\).

Total New Old
Modular forms 10720 10720 0
Cusp forms 10400 10400 0
Eisenstein series 320 320 0

Trace form

\( 10400 q - 117 q^{2} - 62 q^{3} - 169 q^{4} - 123 q^{5} - 51 q^{6} - 39 q^{7} - 66 q^{9} + O(q^{10}) \) \( 10400 q - 117 q^{2} - 62 q^{3} - 169 q^{4} - 123 q^{5} - 51 q^{6} - 39 q^{7} - 66 q^{9} - 176 q^{10} - 129 q^{11} - 149 q^{12} - 39 q^{13} - 123 q^{14} - 27 q^{15} - 169 q^{16} - 66 q^{18} - 126 q^{19} - 141 q^{20} - 121 q^{21} - 33 q^{22} - 90 q^{23} - 237 q^{24} + 81 q^{25} - 77 q^{27} - 156 q^{28} - 162 q^{29} - 72 q^{30} - 41 q^{31} - 132 q^{32} - 59 q^{33} - 34 q^{34} - 127 q^{36} - 164 q^{37} - 369 q^{38} - 206 q^{39} - 70 q^{40} - 117 q^{41} - 84 q^{42} - 44 q^{43} - 57 q^{45} - 136 q^{46} - 123 q^{47} - 221 q^{48} + 77 q^{49} - 192 q^{50} - 351 q^{51} - 39 q^{52} + 242 q^{54} - 158 q^{55} - 222 q^{56} - 159 q^{57} - 15 q^{58} - 216 q^{59} - 92 q^{60} - 39 q^{61} - 235 q^{63} + 72 q^{64} - 132 q^{65} - 93 q^{66} - 42 q^{67} - 312 q^{68} - 40 q^{69} - 74 q^{70} - 269 q^{72} - 156 q^{73} - 117 q^{74} - 76 q^{75} - 143 q^{76} - 561 q^{77} - 202 q^{78} - 39 q^{79} + 10 q^{81} - 174 q^{82} - 72 q^{83} + 113 q^{84} + 27 q^{85} - 60 q^{86} - 55 q^{87} - 84 q^{88} + 4 q^{90} - 360 q^{91} + 507 q^{92} - 27 q^{93} - 50 q^{94} - 261 q^{95} + 90 q^{96} - 68 q^{97} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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