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Properties

Label 160.2.d
Level $160$
Weight $2$
Character orbit 160.d
Rep. character $\chi_{160}(81,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(160, [\chi])\).

Total New Old
Modular forms 32 4 28
Cusp forms 16 4 12
Eisenstein series 16 0 16

Trace form

\( 4 q + 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{7} - 4 q^{9} - 4 q^{15} + 4 q^{23} - 4 q^{25} + 8 q^{31} + 8 q^{33} - 24 q^{39} - 8 q^{41} - 20 q^{47} - 12 q^{49} + 8 q^{55} + 8 q^{57} + 20 q^{63} - 8 q^{71} + 16 q^{73} + 32 q^{79} + 4 q^{81} + 48 q^{87} + 8 q^{89} - 16 q^{95} - 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.2.d.a 160.d 8.b $4$ $1.278$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(1+\zeta_{12}^{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

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