Properties

Label 160.6.f
Level 160
Weight 6
Character orbit f
Rep. character \(\chi_{160}(49,\cdot)\)
Character field \(\Q\)
Dimension 28
Newform subspaces 1
Sturm bound 144
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 160.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(160, [\chi])\).

Total New Old
Modular forms 128 32 96
Cusp forms 112 28 84
Eisenstein series 16 4 12

Trace form

\( 28q + 1940q^{9} + O(q^{10}) \) \( 28q + 1940q^{9} + 488q^{15} + 1556q^{25} - 4368q^{31} - 23360q^{39} - 2480q^{41} - 38420q^{49} + 48776q^{55} + 37200q^{65} + 69232q^{71} + 35984q^{79} + 122596q^{81} - 178744q^{89} - 89416q^{95} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
160.6.f.a \(28\) \(25.661\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{6}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database