Properties

Label 67.2.a
Level 67
Weight 2
Character orbit 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.

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

Trace form

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

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

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 \(-1\) \(1\) \(4\) \(1\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)