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Properties

Label 1728.3.bg
Level $1728$
Weight $3$
Character orbit 1728.bg
Rep. character $\chi_{1728}(163,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2048$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.bg (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1728, [\chi])\).

Total New Old
Modular forms 4656 2048 2608
Cusp forms 4560 2048 2512
Eisenstein series 96 0 96

Trace form

\( 2048 q + O(q^{10}) \) \( 2048 q + 528 q^{52} - 512 q^{55} - 96 q^{64} - 1024 q^{67} - 672 q^{70} + 1664 q^{76} + 512 q^{79} - 1040 q^{82} - 560 q^{88} - 96 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1728, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1728, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1728, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)