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Properties

Label 1089.2.f
Level $1089$
Weight $2$
Character orbit 1089.f
Rep. character $\chi_{1089}(487,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $164$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 624 196 428
Cusp forms 432 164 268
Eisenstein series 192 32 160

Trace form

\( 164 q - 4 q^{2} - 36 q^{4} - 3 q^{5} + 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 164 q - 4 q^{2} - 36 q^{4} - 3 q^{5} + 8 q^{7} + 8 q^{8} + 24 q^{10} + 8 q^{13} - 2 q^{14} - 46 q^{16} + 14 q^{17} + 8 q^{19} + 6 q^{20} + 32 q^{23} - 36 q^{25} - 16 q^{26} - 24 q^{28} - 4 q^{29} - 13 q^{31} - 48 q^{32} - 32 q^{34} + 13 q^{37} - 2 q^{38} + 12 q^{40} + 20 q^{41} + 16 q^{43} + 32 q^{46} + 14 q^{47} + 27 q^{49} + 18 q^{50} - 16 q^{52} + 18 q^{53} + 60 q^{56} + 10 q^{58} - 35 q^{59} - 24 q^{61} - 28 q^{62} - 58 q^{64} - 28 q^{65} - 52 q^{67} - 28 q^{68} + 16 q^{70} - 17 q^{71} - 44 q^{73} - 30 q^{74} - 8 q^{76} - 24 q^{79} - 36 q^{80} + 6 q^{82} + 34 q^{83} - 44 q^{85} + 48 q^{89} - 44 q^{91} - 12 q^{92} + 8 q^{94} + 30 q^{95} + 43 q^{97} + 40 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)