Properties

Label 32.3.f
Level $32$
Weight $3$
Character orbit 32.f
Rep. character $\chi_{32}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 32.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(32, [\chi])\).

Total New Old
Modular forms 20 0 20
Cusp forms 12 0 12
Eisenstein series 8 0 8

Decomposition of \(S_{3}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)