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Properties

Label 1089.2.g
Level $1089$
Weight $2$
Character orbit 1089.g
Rep. character $\chi_{1089}(362,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $200$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 288 232 56
Cusp forms 240 200 40
Eisenstein series 48 32 16

Trace form

\( 200 q + 8 q^{3} - 90 q^{4} + 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 200 q + 8 q^{3} - 90 q^{4} + 12 q^{5} - 12 q^{9} - 30 q^{12} + 6 q^{14} + 26 q^{15} - 70 q^{16} - 30 q^{20} - 42 q^{23} + 76 q^{25} - 10 q^{27} - 4 q^{31} - 10 q^{34} - 14 q^{36} + 20 q^{37} - 96 q^{38} + 14 q^{42} + 42 q^{45} - 18 q^{47} - 60 q^{48} + 54 q^{49} + 90 q^{56} + 6 q^{58} - 12 q^{59} - 6 q^{60} + 72 q^{64} - 8 q^{67} - 90 q^{69} - 20 q^{70} + 30 q^{75} - 4 q^{78} - 20 q^{81} - 12 q^{82} + 96 q^{86} + 12 q^{91} + 72 q^{92} + 98 q^{93} - 10 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)