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Properties

Label 1089.4.bb
Level $1089$
Weight $4$
Character orbit 1089.bb
Rep. character $\chi_{1089}(8,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $5280$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1089.bb (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 363 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1089, [\chi])\).

Total New Old
Modular forms 16000 5280 10720
Cusp forms 15680 5280 10400
Eisenstein series 320 0 320

Trace form

\( 5280 q + 528 q^{4} + O(q^{10}) \) \( 5280 q + 528 q^{4} - 264 q^{10} + 528 q^{13} + 2448 q^{16} - 2388 q^{22} - 4308 q^{25} + 1140 q^{28} + 2940 q^{31} - 648 q^{34} + 576 q^{37} - 1440 q^{40} + 720 q^{46} - 8988 q^{49} - 22380 q^{52} - 8592 q^{55} + 7812 q^{58} + 1320 q^{61} + 12912 q^{64} - 432 q^{67} + 14496 q^{70} + 3516 q^{73} - 1584 q^{79} - 5796 q^{82} - 11400 q^{85} - 1512 q^{88} - 8040 q^{91} - 2280 q^{94} + 7512 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

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