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Properties

Label 161.2.i
Level $161$
Weight $2$
Character orbit 161.i
Rep. character $\chi_{161}(8,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $120$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 161.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 180 120 60
Cusp forms 140 120 20
Eisenstein series 40 0 40

Trace form

\( 120 q - 2 q^{2} - 4 q^{3} - 22 q^{4} - 4 q^{5} - 14 q^{6} - 2 q^{7} - 12 q^{8} - 16 q^{9} + O(q^{10}) \) \( 120 q - 2 q^{2} - 4 q^{3} - 22 q^{4} - 4 q^{5} - 14 q^{6} - 2 q^{7} - 12 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} - 22 q^{12} - 12 q^{13} - 6 q^{14} - 22 q^{15} - 28 q^{16} + 14 q^{17} + 20 q^{18} - 6 q^{19} - 36 q^{20} - 4 q^{21} + 4 q^{23} + 96 q^{24} - 22 q^{25} + 10 q^{26} - 52 q^{27} - 14 q^{28} - 6 q^{29} + 20 q^{30} - 34 q^{31} - 24 q^{32} - 2 q^{33} - 12 q^{34} - 4 q^{35} - 21 q^{36} + 8 q^{37} - 16 q^{38} + 24 q^{39} + 108 q^{40} + 16 q^{41} - 4 q^{42} + 12 q^{43} + 17 q^{44} - 72 q^{45} + 108 q^{46} + 24 q^{47} + 34 q^{48} - 12 q^{49} - 25 q^{50} - 20 q^{51} - 98 q^{52} - 40 q^{53} + 50 q^{54} + 56 q^{55} - 30 q^{56} + 26 q^{57} - 39 q^{58} + 28 q^{59} + 76 q^{60} - 56 q^{61} + 42 q^{62} - 26 q^{63} - 52 q^{65} + 28 q^{66} - 48 q^{67} - 160 q^{68} + 14 q^{69} - 8 q^{70} + 38 q^{71} - 164 q^{72} - 8 q^{73} + 35 q^{74} - 8 q^{75} + 82 q^{76} + 36 q^{77} - 86 q^{78} - 36 q^{79} + 68 q^{80} + 96 q^{81} + 26 q^{82} + 42 q^{83} + 114 q^{84} - 44 q^{85} + 44 q^{86} - 92 q^{87} - 133 q^{88} + 52 q^{89} + 146 q^{90} + 72 q^{91} - 156 q^{92} + 132 q^{93} - 122 q^{94} - 56 q^{95} + 252 q^{96} + 122 q^{97} + 9 q^{98} - 136 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
161.2.i.a 161.i 23.c $50$ $1.286$ None \(2\) \(0\) \(-11\) \(5\) $\mathrm{SU}(2)[C_{11}]$
161.2.i.b 161.i 23.c $70$ $1.286$ None \(-4\) \(-4\) \(7\) \(-7\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(161, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(161, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)