↑

Properties

Label 161.2.g
Level $161$
Weight $2$
Character orbit 161.g
Rep. character $\chi_{161}(45,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 161.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(161, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

Trace form

\( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + O(q^{10}) \) \( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50} + 72 q^{52} - 30 q^{54} + 14 q^{58} - 54 q^{59} - 68 q^{64} + 38 q^{70} + 16 q^{71} - 4 q^{72} - 18 q^{73} + 96 q^{75} + 20 q^{77} - 12 q^{78} + 22 q^{81} - 52 q^{85} - 18 q^{87} - 28 q^{92} - 10 q^{93} + 84 q^{94} + 56 q^{95} - 84 q^{96} - 146 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(161, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.2.g.a 161.g 161.g $28$ $1.286$ None \(-4\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$