Properties

Label 32.2.e
Level $32$
Weight $2$
Character orbit 32.e
Rep. character $\chi_{32}(9,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(32, [\chi])\).

Total New Old
Modular forms 12 0 12
Cusp forms 4 0 4
Eisenstein series 8 0 8

Decomposition of \(S_{2}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

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