Properties

Label 65.2.b
Level 65
Weight 2
Character orbit b
Rep. character \(\chi_{65}(14,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q - 10q^{4} + 4q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 10q^{4} + 4q^{6} - 6q^{9} + 2q^{10} - 12q^{11} + 8q^{14} + 16q^{15} + 10q^{16} - 20q^{20} - 4q^{21} + 16q^{24} + 2q^{25} - 6q^{26} - 12q^{29} + 8q^{30} - 20q^{31} + 20q^{34} + 8q^{35} - 22q^{36} + 8q^{39} - 34q^{40} - 8q^{41} + 40q^{44} - 4q^{45} + 32q^{46} + 18q^{49} + 16q^{50} + 24q^{51} - 68q^{54} - 16q^{55} + 40q^{56} + 16q^{59} - 12q^{60} + 12q^{61} - 66q^{64} - 2q^{65} - 16q^{66} - 24q^{69} - 20q^{70} - 24q^{71} + 4q^{74} + 16q^{75} - 20q^{76} + 32q^{79} + 48q^{80} + 46q^{81} + 12q^{84} - 12q^{85} - 32q^{86} - 20q^{89} + 70q^{90} - 4q^{91} - 32q^{94} + 16q^{95} - 36q^{96} + 16q^{99} + O(q^{100}) \)

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.b.a \(6\) \(0.519\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)