Properties

Label 161.2.a
Level 161
Weight 2
Character orbit a
Rep. character \(\chi_{161}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 4
Sturm bound 32
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 161 = 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 161.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(161))\) into irreducible Hecke orbits

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

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