Properties

Label 160.3.g
Level $160$
Weight $3$
Character orbit 160.g
Rep. character $\chi_{160}(111,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 160.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(160, [\chi])\).

Total New Old
Modular forms 56 8 48
Cusp forms 40 8 32
Eisenstein series 16 0 16

Trace form

\( 8 q + 24 q^{9} + O(q^{10}) \) \( 8 q + 24 q^{9} + 32 q^{11} - 32 q^{19} - 40 q^{25} + 96 q^{27} + 16 q^{33} + 48 q^{41} - 96 q^{43} - 88 q^{49} - 64 q^{51} - 176 q^{57} - 224 q^{59} - 160 q^{67} + 160 q^{73} - 56 q^{81} + 480 q^{83} - 48 q^{89} + 224 q^{97} + 352 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
160.3.g.a 160.g 8.d $8$ $4.360$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(3+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(160, [\chi])\) into lower level spaces

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