Properties

Label 1152.3.bf
Level $1152$
Weight $3$
Character orbit 1152.bf
Rep. character $\chi_{1152}(55,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $0$
Newform subspaces $0$
Sturm bound $576$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.bf (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 0 \)
Sturm bound: \(576\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 3136 0 3136
Cusp forms 3008 0 3008
Eisenstein series 128 0 128

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)