Properties

Label 65.2.k
Level 65
Weight 2
Character orbit k
Rep. character \(\chi_{65}(8,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 10
Newforms 2
Sturm bound 14
Trace bound 1

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Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 65 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 18 18 0
Cusp forms 10 10 0
Eisenstein series 8 8 0

Trace form

\( 10q - 2q^{2} - 4q^{3} + 6q^{4} - 4q^{6} - 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{3} + 6q^{4} - 4q^{6} - 6q^{8} - 8q^{10} + 4q^{11} + 4q^{13} - 10q^{16} - 14q^{17} + 4q^{19} - 20q^{20} - 16q^{21} + 8q^{22} + 20q^{23} - 4q^{24} + 6q^{25} + 12q^{26} + 20q^{27} + 16q^{30} + 12q^{31} + 6q^{32} - 12q^{33} + 2q^{34} - 16q^{35} - 8q^{38} + 4q^{39} + 28q^{40} + 2q^{41} + 20q^{42} + 4q^{43} + 12q^{44} + 2q^{45} + 8q^{46} - 16q^{48} - 18q^{49} - 26q^{50} - 28q^{52} - 14q^{53} - 12q^{54} + 16q^{55} - 60q^{57} + 8q^{59} + 44q^{60} - 8q^{61} + 40q^{62} + 20q^{63} - 34q^{64} - 14q^{65} - 40q^{66} - 20q^{67} + 2q^{68} + 8q^{69} + 28q^{70} - 8q^{71} - 24q^{73} - 44q^{75} + 16q^{76} + 20q^{77} + 40q^{78} + 4q^{80} - 10q^{81} - 34q^{82} + 20q^{84} - 18q^{85} - 48q^{86} + 16q^{87} + 16q^{88} - 18q^{89} + 10q^{90} + 28q^{91} + 44q^{92} + 28q^{95} + 40q^{96} + 16q^{97} + 98q^{98} + O(q^{100}) \)

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.k.a \(2\) \(0.519\) \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-2\) \(0\) \(q+q^{2}+(1+i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
65.2.k.b \(8\) \(0.519\) 8.0.619810816.2 None \(-4\) \(-6\) \(2\) \(0\) \(q+\beta _{5}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)