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Properties

Label 567.3.j
Level $567$
Weight $3$
Character orbit 567.j
Rep. character $\chi_{567}(296,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $124$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 567.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(216\)

Dimensions

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

Total New Old
Modular forms 312 132 180
Cusp forms 264 124 140
Eisenstein series 48 8 40

Trace form

\( 124 q - 236 q^{4} + 7 q^{7} + O(q^{10}) \) \( 124 q - 236 q^{4} + 7 q^{7} - 18 q^{10} + 29 q^{13} + 436 q^{16} + 68 q^{19} + 12 q^{22} + 268 q^{25} - 20 q^{28} + 164 q^{31} + 12 q^{34} + 53 q^{37} + 120 q^{40} + 164 q^{43} - 42 q^{46} + 19 q^{49} - 250 q^{52} - 228 q^{55} - 114 q^{58} + 194 q^{61} - 728 q^{64} + 14 q^{67} - 252 q^{70} - 16 q^{73} - 580 q^{76} + 458 q^{79} + 6 q^{82} + 114 q^{85} + 78 q^{88} + 131 q^{91} - 636 q^{94} - 91 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(567, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)