Properties

Label 1089.2.bb
Level $1089$
Weight $2$
Character orbit 1089.bb
Rep. character $\chi_{1089}(8,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $1760$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.bb (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 5440 1760 3680
Cusp forms 5120 1760 3360
Eisenstein series 320 0 320

Trace form

\( 1760 q + 44 q^{4} + O(q^{10}) \) \( 1760 q + 44 q^{4} - 44 q^{10} - 44 q^{13} + 60 q^{16} + 136 q^{22} - 8 q^{25} - 40 q^{28} - 60 q^{31} - 8 q^{34} + 4 q^{37} - 60 q^{40} + 40 q^{46} + 64 q^{49} + 84 q^{52} + 160 q^{55} - 72 q^{58} + 116 q^{64} - 32 q^{67} + 20 q^{70} - 24 q^{73} + 88 q^{79} - 84 q^{82} + 100 q^{85} + 12 q^{88} + 72 q^{91} + 80 q^{94} - 52 q^{97} + O(q^{100}) \)

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

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