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Properties

Label 160.6.d
Level $160$
Weight $6$
Character orbit 160.d
Rep. character $\chi_{160}(81,\cdot)$
Character field $\Q$
Dimension $20$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
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 20 108
Cusp forms 112 20 92
Eisenstein series 16 0 16

Trace form

\( 20 q + 196 q^{7} - 1620 q^{9} + O(q^{10}) \) \( 20 q + 196 q^{7} - 1620 q^{9} - 900 q^{15} + 4676 q^{23} - 12500 q^{25} - 7160 q^{31} + 5672 q^{33} + 44904 q^{39} + 11608 q^{41} - 44180 q^{47} + 18756 q^{49} + 24200 q^{55} + 5032 q^{57} - 240620 q^{63} + 200312 q^{71} - 105136 q^{73} - 282080 q^{79} + 65172 q^{81} + 332592 q^{87} - 3160 q^{89} - 144400 q^{95} + 147376 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.6.d.a 160.d 8.b $20$ $25.661$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(196\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(10+\beta _{4})q^{7}+(-3^{4}+\cdots)q^{9}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)