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

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

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 \(2\) \(-8\) \(-6\) \(2\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)