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Properties

Label 1089.6.bb
Level $1089$
Weight $6$
Character orbit 1089.bb
Rep. character $\chi_{1089}(8,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $8800$
Sturm bound $792$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1089.bb (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1089, [\chi])\).

Total New Old
Modular forms 26560 8800 17760
Cusp forms 26240 8800 17440
Eisenstein series 320 0 320

Trace form

\( 8800 q + 3520 q^{4} + O(q^{10}) \) \( 8800 q + 3520 q^{4} + 5456 q^{10} - 5764 q^{13} + 46992 q^{16} + 32612 q^{22} - 129184 q^{25} - 380 q^{28} - 38412 q^{31} + 31064 q^{34} - 16852 q^{37} + 119040 q^{40} - 104800 q^{46} - 428824 q^{49} + 73236 q^{52} + 387584 q^{55} + 39996 q^{58} - 155760 q^{61} + 620752 q^{64} + 208736 q^{67} + 299992 q^{70} + 370224 q^{73} - 807400 q^{79} - 131604 q^{82} + 892700 q^{85} - 99048 q^{88} + 564168 q^{91} - 492920 q^{94} - 751388 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)