Properties

Label 161.2.o
Level $161$
Weight $2$
Character orbit 161.o
Rep. character $\chi_{161}(5,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $280$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 161.o (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{66})\)
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 360 360 0
Cusp forms 280 280 0
Eisenstein series 80 80 0

Trace form

\( 280 q - 7 q^{2} - 27 q^{3} + q^{4} - 33 q^{5} - 22 q^{7} - 56 q^{8} - 15 q^{9} + O(q^{10}) \) \( 280 q - 7 q^{2} - 27 q^{3} + q^{4} - 33 q^{5} - 22 q^{7} - 56 q^{8} - 15 q^{9} - 33 q^{10} - 11 q^{11} - 39 q^{12} - 22 q^{14} - 44 q^{15} + 11 q^{16} - 33 q^{17} - 77 q^{18} - 33 q^{19} + 44 q^{21} + 11 q^{23} - 30 q^{24} - 11 q^{25} - 21 q^{26} + 66 q^{28} + 33 q^{30} - 33 q^{31} - 27 q^{32} - 33 q^{33} + 10 q^{35} + 66 q^{36} - 55 q^{37} - 33 q^{38} + 5 q^{39} - 33 q^{40} + 88 q^{42} + 44 q^{43} - 66 q^{44} - 29 q^{46} - 30 q^{47} + 16 q^{49} + 26 q^{50} - 55 q^{51} - 105 q^{52} - 11 q^{53} - 3 q^{54} + 99 q^{56} + 44 q^{57} - 36 q^{58} + 21 q^{59} - 11 q^{60} - 33 q^{61} + 33 q^{63} + 24 q^{64} + 66 q^{65} + 66 q^{66} - 11 q^{67} + 6 q^{70} - 60 q^{71} + 59 q^{72} - 15 q^{73} - 129 q^{75} + 13 q^{77} - 252 q^{78} + 33 q^{79} + 264 q^{80} + 99 q^{81} - 33 q^{82} + 44 q^{84} - 212 q^{85} + 11 q^{86} + 381 q^{87} + 198 q^{88} - 33 q^{89} - 214 q^{92} - 12 q^{93} + 180 q^{94} + 32 q^{95} + 51 q^{96} + 80 q^{98} - 198 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.2.o.a 161.o 161.o $280$ $1.286$ None 161.2.o.a \(-7\) \(-27\) \(-33\) \(-22\) $\mathrm{SU}(2)[C_{66}]$