Properties

Label 67.2.c
Level 67
Weight 2
Character orbit c
Rep. character \(\chi_{67}(29,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 10
Newforms 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 67.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(67, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10q + 2q^{2} - 8q^{3} - 4q^{4} - 6q^{5} - 6q^{6} + 2q^{7} - 12q^{8} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 8q^{3} - 4q^{4} - 6q^{5} - 6q^{6} + 2q^{7} - 12q^{8} + 10q^{9} + 3q^{10} + 2q^{11} + 7q^{12} + 10q^{14} - 2q^{15} + 6q^{16} - 6q^{17} + 6q^{18} - 7q^{20} - 2q^{21} - 16q^{22} + 2q^{23} + 42q^{24} + 12q^{25} + 5q^{26} - 50q^{27} + 11q^{28} - 8q^{29} - 35q^{30} + 12q^{31} - q^{32} - 14q^{33} + 28q^{34} - 21q^{35} - 22q^{36} - 7q^{37} + 5q^{38} + 17q^{39} - 10q^{40} + 16q^{41} + 16q^{42} + 20q^{43} - 3q^{44} + 18q^{45} - 19q^{46} + 17q^{47} + 16q^{48} + 5q^{49} + 20q^{50} - 32q^{52} + 8q^{53} - 18q^{54} - 2q^{55} - 8q^{56} + 14q^{57} - 32q^{58} + 6q^{59} + 42q^{60} - 6q^{61} + 8q^{62} + 8q^{63} - 12q^{64} - 18q^{65} + 6q^{66} - 10q^{67} + 94q^{68} + 23q^{69} - 44q^{70} + 3q^{71} - 106q^{72} - 34q^{73} - 20q^{74} - 46q^{75} - 32q^{76} + 3q^{77} - 2q^{78} + 8q^{79} - 31q^{80} + 50q^{81} + 42q^{82} + 28q^{83} + 3q^{84} - 16q^{85} + 9q^{86} + 27q^{87} - 19q^{88} - 84q^{89} + 77q^{90} + 68q^{91} + 18q^{92} + q^{93} - 48q^{94} + 31q^{95} + 19q^{96} - 20q^{97} + 21q^{98} + 31q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(67, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
67.2.c.a \(10\) \(0.535\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-8\) \(-6\) \(2\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)