Properties

Label 160.6.o
Level 160
Weight 6
Character orbit o
Rep. character \(\chi_{160}(47,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 56
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.o (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 256 64 192
Cusp forms 224 56 168
Eisenstein series 32 8 24

Trace form

\( 56q + 4q^{3} + O(q^{10}) \) \( 56q + 4q^{3} + 8q^{11} - 408q^{17} - 3120q^{25} - 968q^{27} - 976q^{33} + 4780q^{35} - 8q^{41} - 1308q^{43} - 20872q^{51} + 968q^{57} + 17680q^{65} - 89252q^{67} - 25184q^{73} + 127740q^{75} - 67792q^{81} + 126444q^{83} - 329432q^{91} + 212576q^{97} + O(q^{100}) \)

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.o.a \(56\) \(25.661\) None \(0\) \(4\) \(0\) \(0\)

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