Properties

Label 65.2.e
Level 65
Weight 2
Character orbit e
Rep. character \(\chi_{65}(16,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 8
Newforms 2
Sturm bound 14
Trace bound 2

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(65, [\chi])\).

Total New Old
Modular forms 16 8 8
Cusp forms 8 8 0
Eisenstein series 8 0 8

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(65, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
65.2.e.a \(4\) \(0.519\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(0\) \(4\) \(-4\) \(q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.e.b \(4\) \(0.519\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(-2\) \(-4\) \(2\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)