Properties

Label 160.4.d
Level $160$
Weight $4$
Character orbit 160.d
Rep. character $\chi_{160}(81,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(160, [\chi])\).

Total New Old
Modular forms 80 12 68
Cusp forms 64 12 52
Eisenstein series 16 0 16

Trace form

\( 12 q - 28 q^{7} - 108 q^{9} + O(q^{10}) \) \( 12 q - 28 q^{7} - 108 q^{9} + 60 q^{15} - 604 q^{23} - 300 q^{25} + 264 q^{31} - 232 q^{33} - 600 q^{39} + 40 q^{41} + 940 q^{47} + 1308 q^{49} - 440 q^{55} - 680 q^{57} + 1300 q^{63} + 1592 q^{71} + 432 q^{73} - 2016 q^{79} + 2508 q^{81} + 1968 q^{87} - 424 q^{89} + 1520 q^{95} - 1584 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.4.d.a 160.d 8.b $12$ $9.440$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-2+\beta _{4})q^{7}+(-9+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(160, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)