Properties

Label 167.2.a
Level $167$
Weight $2$
Character orbit 167.a
Rep. character $\chi_{167}(1,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\) into newform subspaces

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 \(2\) \(3\) \(4\) \(11\) \(-\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)