Properties

Label 1089.3.h
Level $1089$
Weight $3$
Character orbit 1089.h
Rep. character $\chi_{1089}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $416$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1089.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1089, [\chi])\).

Total New Old
Modular forms 552 448 104
Cusp forms 504 416 88
Eisenstein series 48 32 16

Trace form

\( 416 q + 2 q^{3} + 402 q^{4} - 4 q^{5} + 18 q^{9} + O(q^{10}) \) \( 416 q + 2 q^{3} + 402 q^{4} - 4 q^{5} + 18 q^{9} - 90 q^{12} + 18 q^{14} + 26 q^{15} - 742 q^{16} - 22 q^{20} + 46 q^{23} - 884 q^{25} + 136 q^{26} + 134 q^{27} - 28 q^{31} - 64 q^{34} + 124 q^{36} - 76 q^{37} + 30 q^{38} + 134 q^{42} - 330 q^{45} + 14 q^{47} - 414 q^{48} + 1122 q^{49} + 320 q^{53} + 266 q^{56} - 30 q^{58} - 142 q^{59} + 150 q^{60} - 2472 q^{64} + 154 q^{67} - 390 q^{69} - 260 q^{70} - 508 q^{71} - 324 q^{75} + 308 q^{78} - 1232 q^{80} + 106 q^{81} + 216 q^{82} - 522 q^{86} + 280 q^{89} + 372 q^{91} - 876 q^{92} - 526 q^{93} + 284 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

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