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Properties

Label 567.3.m
Level $567$
Weight $3$
Character orbit 567.m
Rep. character $\chi_{567}(82,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 567.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 312 136 176
Cusp forms 264 120 144
Eisenstein series 48 16 32

Trace form

\( 120 q - 110 q^{4} + 8 q^{7} + O(q^{10}) \) \( 120 q - 110 q^{4} + 8 q^{7} - 12 q^{10} - 170 q^{16} - 12 q^{19} + 160 q^{22} + 222 q^{25} - 64 q^{28} + 102 q^{31} - 26 q^{37} + 204 q^{40} + 112 q^{43} + 88 q^{46} - 156 q^{49} - 42 q^{52} - 218 q^{58} - 252 q^{61} + 320 q^{64} + 48 q^{67} + 234 q^{70} - 408 q^{73} + 336 q^{79} - 36 q^{82} + 300 q^{85} - 394 q^{88} - 174 q^{91} - 282 q^{94} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(567, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)