Properties

Label 1152.3.bn
Level $1152$
Weight $3$
Character orbit 1152.bn
Rep. character $\chi_{1152}(53,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $2048$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.bn (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 384 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

Total New Old
Modular forms 6208 2048 4160
Cusp forms 6080 2048 4032
Eisenstein series 128 0 128

Trace form

\( 2048q + O(q^{10}) \) \( 2048q - 2112q^{52} + 384q^{64} + 2688q^{70} + 832q^{76} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)