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Properties

Label 160.3.m
Level $160$
Weight $3$
Character orbit 160.m
Rep. character $\chi_{160}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
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 112 28 84
Cusp forms 80 20 60
Eisenstein series 32 8 24

Trace form

\( 20 q + 4 q^{7} + O(q^{10}) \) \( 20 q + 4 q^{7} + 4 q^{15} - 12 q^{17} + 4 q^{23} - 28 q^{25} + 136 q^{31} + 32 q^{33} - 8 q^{41} - 188 q^{47} - 96 q^{55} - 40 q^{57} - 228 q^{63} - 60 q^{65} - 248 q^{71} - 124 q^{73} + 132 q^{81} + 488 q^{87} + 488 q^{95} + 100 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.m.a 160.m 40.i $20$ $4.360$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{8}q^{3}+\beta _{9}q^{5}-\beta _{4}q^{7}+(2\beta _{2}-\beta _{13}+\cdots)q^{9}+\cdots\)

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

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