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Properties

Label 567.3.bf
Level $567$
Weight $3$
Character orbit 567.bf
Rep. character $\chi_{567}(44,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $276$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 567.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(567, [\chi])\).

Total New Old
Modular forms 900 300 600
Cusp forms 828 276 552
Eisenstein series 72 24 48

Trace form

\( 276 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 18 q^{8} + O(q^{10}) \) \( 276 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 18 q^{8} - 6 q^{10} - 15 q^{11} - 12 q^{13} + 15 q^{14} + 9 q^{16} - 6 q^{19} + 24 q^{20} - 12 q^{22} - 96 q^{23} - 3 q^{25} - 12 q^{28} - 96 q^{29} - 3 q^{31} + 189 q^{32} - 234 q^{35} + 3 q^{37} + 141 q^{38} - 120 q^{40} + 156 q^{41} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 105 q^{47} - 78 q^{49} + 375 q^{50} - 27 q^{52} - 405 q^{53} - 24 q^{55} + 627 q^{56} - 3 q^{58} - 42 q^{59} + 285 q^{61} - 873 q^{62} + 762 q^{64} + 183 q^{65} - 3 q^{67} - 396 q^{68} - 456 q^{70} - 306 q^{71} - 123 q^{73} + 447 q^{74} - 60 q^{76} + 15 q^{77} - 21 q^{79} + 576 q^{80} - 6 q^{82} + 372 q^{83} - 117 q^{85} - 267 q^{86} - 411 q^{88} + 96 q^{91} + 1572 q^{92} + 501 q^{94} - 273 q^{95} - 12 q^{97} - 639 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(567, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)