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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 23
161.2.a.a \(1\) \(1.286\) \(\Q\) None \(-1\) \(0\) \(2\) \(1\) \(-\) \(+\) \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
161.2.a.b \(2\) \(1.286\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
161.2.a.c \(3\) \(1.286\) 3.3.148.1 None \(-1\) \(2\) \(2\) \(-3\) \(+\) \(-\) \(q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
161.2.a.d \(5\) \(1.286\) 5.5.2147108.1 None \(2\) \(0\) \(-4\) \(5\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

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

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