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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

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

Display 100 coefficients 10 coefficients

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

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