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Properties

Label 1089.2.v
Level $1089$
Weight $2$
Character orbit 1089.v
Rep. character $\chi_{1089}(37,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $2160$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.v (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 5440 2240 3200
Cusp forms 5120 2160 2960
Eisenstein series 320 80 240

Trace form

\( 2160 q + 40 q^{2} + 10 q^{4} + 39 q^{5} - 36 q^{7} + 52 q^{8} + O(q^{10}) \) \( 2160 q + 40 q^{2} + 10 q^{4} + 39 q^{5} - 36 q^{7} + 52 q^{8} - 42 q^{10} + 53 q^{11} - 47 q^{13} + 72 q^{14} - 2 q^{16} + 58 q^{17} - 36 q^{19} + 50 q^{20} - 112 q^{22} + 50 q^{23} + q^{25} + 60 q^{26} - 68 q^{28} + 40 q^{29} - 69 q^{31} - 4 q^{32} - 36 q^{34} + 44 q^{35} - 40 q^{38} + 45 q^{40} + 64 q^{41} - 28 q^{43} + 89 q^{44} - 12 q^{46} + 58 q^{47} + 194 q^{50} - 214 q^{52} + 68 q^{53} - 140 q^{55} + 125 q^{56} - 95 q^{58} + 27 q^{59} - 68 q^{61} + 71 q^{62} - 28 q^{64} + 49 q^{65} + 23 q^{67} + 16 q^{68} - 124 q^{70} + 81 q^{71} - 110 q^{73} + 14 q^{74} + 168 q^{76} - 90 q^{77} - 68 q^{79} - 113 q^{80} - 86 q^{82} + 78 q^{83} + 22 q^{85} + 60 q^{86} + 153 q^{88} + 17 q^{89} + 39 q^{91} + 34 q^{92} + 151 q^{94} - 14 q^{95} + 70 q^{97} + 84 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)