Properties

Label 161.4.m
Level $161$
Weight $4$
Character orbit 161.m
Rep. character $\chi_{161}(2,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $920$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 161.m (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(161, [\chi])\).

Total New Old
Modular forms 1000 1000 0
Cusp forms 920 920 0
Eisenstein series 80 80 0

Trace form

\( 920 q - 7 q^{2} - 9 q^{3} + 157 q^{4} + 3 q^{5} - 52 q^{6} - 22 q^{7} - 32 q^{8} + 397 q^{9} - q^{10} - 29 q^{11} - 101 q^{12} - 36 q^{13} + 134 q^{14} - 320 q^{15} + 1157 q^{16} - q^{17} - 81 q^{18}+ \cdots + 3640 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(161, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.4.m.a 161.m 161.m $920$ $9.499$ None 161.4.m.a \(-7\) \(-9\) \(3\) \(-22\) $\mathrm{SU}(2)[C_{33}]$