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Properties

Label 161.2.m
Level $161$
Weight $2$
Character orbit 161.m
Rep. character $\chi_{161}(2,\cdot)$
Character field $\Q(\zeta_{33})$
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.m (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
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

\( 280 q - 11 q^{2} - 9 q^{3} + q^{4} - 11 q^{5} - 52 q^{6} - 20 q^{7} - 32 q^{8} + 5 q^{9} + O(q^{10}) \) \( 280 q - 11 q^{2} - 9 q^{3} + q^{4} - 11 q^{5} - 52 q^{6} - 20 q^{7} - 32 q^{8} + 5 q^{9} - 21 q^{10} - 7 q^{11} - 17 q^{12} - 36 q^{13} - 18 q^{14} - 32 q^{15} + 11 q^{16} - 21 q^{17} + 23 q^{18} - 13 q^{19} + 36 q^{20} - 90 q^{21} - 48 q^{22} + 11 q^{23} - 2 q^{24} + 9 q^{25} + 17 q^{26} + 6 q^{27} - 80 q^{28} - 40 q^{29} + 41 q^{30} - 7 q^{31} + 9 q^{32} - 33 q^{33} - 76 q^{34} - 6 q^{35} - 234 q^{36} + 27 q^{37} + 89 q^{38} + q^{39} - 35 q^{40} - 72 q^{41} + 62 q^{42} - 128 q^{43} + 30 q^{44} + 108 q^{45} - 11 q^{46} - 6 q^{47} + 68 q^{48} + 80 q^{49} - 226 q^{50} + 21 q^{51} + 189 q^{52} - 21 q^{53} + 55 q^{54} - 48 q^{55} + 83 q^{56} - 76 q^{57} + 10 q^{58} + 47 q^{59} - 15 q^{60} + 65 q^{61} + 4 q^{62} + 25 q^{63} + 24 q^{64} - 66 q^{65} - 44 q^{66} - 21 q^{67} + 202 q^{68} - 60 q^{69} - 6 q^{70} - 28 q^{71} - 129 q^{72} + 15 q^{73} - 34 q^{74} + 139 q^{75} - 44 q^{76} + 61 q^{77} + 244 q^{78} - 69 q^{79} - 102 q^{80} + 151 q^{81} + 137 q^{82} + 24 q^{83} + 32 q^{84} + 124 q^{85} - 55 q^{86} - 129 q^{87} + 64 q^{88} - 21 q^{89} - 28 q^{90} - 62 q^{91} + 154 q^{92} + 4 q^{93} - 98 q^{94} + 38 q^{95} + 165 q^{96} - 12 q^{97} + 12 q^{98} + 202 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.2.m.a 161.m 161.m $280$ $1.286$ None 161.2.m.a \(-11\) \(-9\) \(-11\) \(-20\) $\mathrm{SU}(2)[C_{33}]$