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Properties

Label 1089.2.u
Level $1089$
Weight $2$
Character orbit 1089.u
Rep. character $\chi_{1089}(34,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $2600$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.u (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1089 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 2680 2680 0
Cusp forms 2600 2600 0
Eisenstein series 80 80 0

Trace form

\( 2600 q - 11 q^{2} - 42 q^{3} + 119 q^{4} - 9 q^{5} - 2 q^{6} - 9 q^{7} - 32 q^{8} - 38 q^{9} + O(q^{10}) \) \( 2600 q - 11 q^{2} - 42 q^{3} + 119 q^{4} - 9 q^{5} - 2 q^{6} - 9 q^{7} - 32 q^{8} - 38 q^{9} - 44 q^{10} - 7 q^{11} - 49 q^{12} - 9 q^{13} - 17 q^{14} + 27 q^{15} + 119 q^{16} - 32 q^{17} - 4 q^{18} - 48 q^{19} - 21 q^{20} + 15 q^{21} - 11 q^{22} - 3 q^{23} - 18 q^{24} + 113 q^{25} - 92 q^{26} - 30 q^{27} - 60 q^{28} - 23 q^{29} - 66 q^{30} - 9 q^{31} - 23 q^{32} + 9 q^{33} + q^{34} - 44 q^{35} - 32 q^{36} - 36 q^{37} - 57 q^{38} + 51 q^{39} - 10 q^{40} - 23 q^{41} - 5 q^{42} - 3 q^{43} - 64 q^{44} + 25 q^{45} - 44 q^{46} - 21 q^{47} + 51 q^{48} + 109 q^{49} - 5 q^{50} - 120 q^{51} - 21 q^{52} + 76 q^{53} - 280 q^{54} - 38 q^{55} + 21 q^{56} - 29 q^{57} - 29 q^{58} + 15 q^{59} - 63 q^{60} - 9 q^{61} + 16 q^{62} + 58 q^{63} - 292 q^{64} - 29 q^{65} + 32 q^{66} - 3 q^{67} + 7 q^{68} + 55 q^{69} - 23 q^{70} - 100 q^{71} - 282 q^{72} - 72 q^{73} - 65 q^{74} - 31 q^{75} - 90 q^{76} - 135 q^{77} - 84 q^{78} - 9 q^{79} - 544 q^{80} - 38 q^{81} - 56 q^{82} - 11 q^{83} - 110 q^{84} - 53 q^{85} - 55 q^{86} + 11 q^{87} - 110 q^{88} + 58 q^{89} - 268 q^{90} + 44 q^{91} - 91 q^{92} + 4 q^{93} - 52 q^{94} - 135 q^{95} + 79 q^{96} + 9 q^{97} + 96 q^{98} + 82 q^{99} + O(q^{100}) \)

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.