Properties

Label 167.2.a
Level 167
Weight 2
Character orbit a
Rep. character \(\chi_{167}(1,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 2
Sturm bound 28
Trace bound 1

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Defining parameters

Level: \( N \) = \( 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 167.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(167))\).

Total New Old
Modular forms 15 15 0
Cusp forms 14 14 0
Eisenstein series 1 1 0

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

\(167\)Dim.
\(+\)\(2\)
\(-\)\(12\)

Trace form

\(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 14q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 14q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut -\mathstrut 10q^{20} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 26q^{24} \) \(\mathstrut +\mathstrut 30q^{25} \) \(\mathstrut -\mathstrut 32q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 16q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 44q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut -\mathstrut 27q^{36} \) \(\mathstrut +\mathstrut 22q^{37} \) \(\mathstrut -\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 35q^{42} \) \(\mathstrut -\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 2q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 36q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 11q^{62} \) \(\mathstrut +\mathstrut 32q^{63} \) \(\mathstrut +\mathstrut 17q^{64} \) \(\mathstrut +\mathstrut 34q^{65} \) \(\mathstrut +\mathstrut 44q^{66} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 10q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 6q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 12q^{75} \) \(\mathstrut +\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 18q^{78} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 14q^{85} \) \(\mathstrut +\mathstrut 64q^{86} \) \(\mathstrut -\mathstrut 46q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 14q^{89} \) \(\mathstrut +\mathstrut 42q^{90} \) \(\mathstrut +\mathstrut 10q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut -\mathstrut 46q^{94} \) \(\mathstrut -\mathstrut 52q^{95} \) \(\mathstrut -\mathstrut 18q^{96} \) \(\mathstrut +\mathstrut 52q^{97} \) \(\mathstrut +\mathstrut 76q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 167
167.2.a.a \(2\) \(1.334\) \(\Q(\sqrt{5}) \) None \(-1\) \(-1\) \(-2\) \(-5\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
167.2.a.b \(12\) \(1.334\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(3\) \(4\) \(11\) \(-\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)