Properties

Label 40.6.j
Level 40
Weight 6
Character orbit j
Rep. character \(\chi_{40}(7,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 0
Newform subspaces 0
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 40.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(40, [\chi])\).

Total New Old
Modular forms 68 0 68
Cusp forms 52 0 52
Eisenstein series 16 0 16

Decomposition of \(S_{6}^{\mathrm{old}}(40, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(40, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database