Properties

Label 729.6.g
Level $729$
Weight $6$
Character orbit 729.g
Rep. character $\chi_{729}(28,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $3168$
Sturm bound $486$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(486\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(729, [\chi])\).

Total New Old
Modular forms 7452 3312 4140
Cusp forms 7128 3168 3960
Eisenstein series 324 144 180

Trace form

\( 3168 q + 36 q^{4} + 36 q^{7} - 72 q^{10} + 36 q^{13} + 36 q^{16} - 72 q^{19} + 36 q^{22} + 36 q^{25} - 36 q^{28} + 36 q^{31} + 36 q^{34} - 72 q^{37} + 36 q^{40} + 36 q^{43} - 72 q^{46} + 36 q^{49} - 540 q^{52}+ \cdots - 476838 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(729, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(729, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(729, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)