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Properties

Label 864.3.x
Level $864$
Weight $3$
Character orbit 864.x
Rep. character $\chi_{864}(53,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $512$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

Total New Old
Modular forms 1176 512 664
Cusp forms 1128 512 616
Eisenstein series 48 0 48

Trace form

\( 512 q + O(q^{10}) \) \( 512 q + 40 q^{10} + 64 q^{16} - 112 q^{22} - 224 q^{40} - 32 q^{46} - 104 q^{52} - 256 q^{55} + 352 q^{58} + 64 q^{61} + 48 q^{64} - 512 q^{67} + 336 q^{70} - 832 q^{76} + 520 q^{82} + 280 q^{88} - 192 q^{91} + 456 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)