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Properties

Label 1089.3.k
Level $1089$
Weight $3$
Character orbit 1089.k
Rep. character $\chi_{1089}(118,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $344$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1089.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 1152 376 776
Cusp forms 960 344 616
Eisenstein series 192 32 160

Trace form

\( 344 q - 5 q^{2} + 173 q^{4} - 11 q^{5} - 10 q^{7} - 25 q^{8} + O(q^{10}) \) \( 344 q - 5 q^{2} + 173 q^{4} - 11 q^{5} - 10 q^{7} - 25 q^{8} + 20 q^{13} - 8 q^{14} - 167 q^{16} - 10 q^{17} - 25 q^{19} + 130 q^{20} + 204 q^{23} - 305 q^{25} + 56 q^{26} + 160 q^{28} + 120 q^{29} - 79 q^{31} - 306 q^{34} - 240 q^{35} - 91 q^{37} - 236 q^{38} - 420 q^{40} - 200 q^{41} + 290 q^{46} - 246 q^{47} + 446 q^{49} + 285 q^{50} + 570 q^{52} + 532 q^{53} + 1296 q^{56} + 492 q^{58} + 136 q^{59} - 130 q^{61} + 240 q^{62} - 415 q^{64} - 126 q^{67} - 180 q^{68} - 496 q^{70} - 139 q^{71} + 220 q^{73} - 1000 q^{74} - 310 q^{79} - 1330 q^{80} - 191 q^{82} + 35 q^{83} + 240 q^{85} + 973 q^{86} + 570 q^{89} + 388 q^{91} - 194 q^{92} - 800 q^{94} + 330 q^{95} - 322 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)