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Properties

Label 161.2.a
Level $161$
Weight $2$
Character orbit 161.a
Rep. character $\chi_{161}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(161))\).

Total New Old
Modular forms 18 11 7
Cusp forms 15 11 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(7\)\(23\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(6\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(161))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 23
161.2.a.a 161.a 1.a $1$ $1.286$ \(\Q\) None \(-1\) \(0\) \(2\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
161.2.a.b 161.a 1.a $2$ $1.286$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
161.2.a.c 161.a 1.a $3$ $1.286$ 3.3.148.1 None \(-1\) \(2\) \(2\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
161.2.a.d 161.a 1.a $5$ $1.286$ 5.5.2147108.1 None \(2\) \(0\) \(-4\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(161))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(161)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)