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Properties

Label 67.2.a
Level $67$
Weight $2$
Character orbit 67.a
Rep. character $\chi_{67}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $11$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 67.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(11\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(67))\).

Total New Old
Modular forms 6 6 0
Cusp forms 5 5 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.

\(67\)Dim
\(+\)\(2\)
\(-\)\(3\)

Trace form

\( 5 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{7} - 6 q^{8} - q^{9} + O(q^{10}) \) \( 5 q - 2 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{14} + 2 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 3 q^{19} - 2 q^{20} - 4 q^{21} - 14 q^{22} + 13 q^{23} - 6 q^{24} + 15 q^{25} + 10 q^{26} + 2 q^{27} - 26 q^{28} - q^{29} - 10 q^{30} - 12 q^{31} - 14 q^{32} + 14 q^{33} + 2 q^{34} + 6 q^{35} - 20 q^{36} + q^{37} + 28 q^{38} + 16 q^{39} + 28 q^{40} + 2 q^{41} + 8 q^{42} - 8 q^{43} + 6 q^{44} - 12 q^{45} + 10 q^{46} - 23 q^{47} + 2 q^{48} - 5 q^{49} - 38 q^{50} + 6 q^{51} + 14 q^{52} - 8 q^{53} - 6 q^{54} - 4 q^{55} + 38 q^{56} - 26 q^{57} + 14 q^{58} + 9 q^{59} - 18 q^{60} - 18 q^{61} - 2 q^{62} + 16 q^{63} + 18 q^{65} + 18 q^{66} + q^{67} + 14 q^{68} - 8 q^{69} - 46 q^{70} + 12 q^{71} + 22 q^{72} + q^{73} + 8 q^{74} - 26 q^{75} - 4 q^{76} - 6 q^{77} - 16 q^{78} - 26 q^{79} - 68 q^{80} - 11 q^{81} + 12 q^{82} + 2 q^{83} + 30 q^{84} + 46 q^{85} - 24 q^{86} + 24 q^{87} - 20 q^{88} - 9 q^{89} + 4 q^{90} - 26 q^{91} + 48 q^{92} + 38 q^{93} + 24 q^{94} - 16 q^{95} + 38 q^{96} + 2 q^{97} - 24 q^{98} - 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 67
67.2.a.a 67.a 1.a $1$ $0.535$ \(\Q\) None \(2\) \(-2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+2q^{5}-4q^{6}+\cdots\)
67.2.a.b 67.a 1.a $2$ $0.535$ \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-6\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
67.2.a.c 67.a 1.a $2$ $0.535$ \(\Q(\sqrt{5}) \) None \(-1\) \(1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)