Properties

Label 67.2.a
Level 67
Weight 2
Character orbit a
Rep. character \(\chi_{67}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 67
67.2.a.a \(1\) \(0.535\) \(\Q\) None \(2\) \(-2\) \(2\) \(-2\) \(-\) \(q+2q^{2}-2q^{3}+2q^{4}+2q^{5}-4q^{6}+\cdots\)
67.2.a.b \(2\) \(0.535\) \(\Q(\sqrt{5}) \) None \(-3\) \(-3\) \(-6\) \(-1\) \(+\) \(q+(-1-\beta )q^{2}+(-2+\beta )q^{3}+3\beta q^{4}+\cdots\)
67.2.a.c \(2\) \(0.535\) \(\Q(\sqrt{5}) \) None \(-1\) \(1\) \(4\) \(1\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)