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Properties

Label 161.2.e
Level $161$
Weight $2$
Character orbit 161.e
Rep. character $\chi_{161}(93,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $2$
Sturm bound $32$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 161 = 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 161.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

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

Trace form

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

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.e.a 161.e 7.c $14$ $1.286$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-5\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{6}-\beta _{10}-\beta _{11}+\cdots)q^{3}+\cdots\)
161.2.e.b 161.e 7.c $14$ $1.286$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(3\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{5}-\beta _{12})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)