Properties

Label 32.2.e
Level 32
Weight 2
Character orbit 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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database