Properties

Label 65.2.t
Level 65
Weight 2
Character orbit t
Rep. character \(\chi_{65}(7,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 20
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.t (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 65 \)
Character field: \(\Q(\zeta_{12})\)
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 36 36 0
Cusp forms 20 20 0
Eisenstein series 16 16 0

Trace form

\( 20q - 6q^{2} - 2q^{3} + 6q^{4} - 8q^{6} - 2q^{7} + 12q^{9} + O(q^{10}) \) \( 20q - 6q^{2} - 2q^{3} + 6q^{4} - 8q^{6} - 2q^{7} + 12q^{9} - 2q^{10} - 16q^{11} - 24q^{12} - 4q^{13} - 20q^{15} - 2q^{16} + 4q^{17} - 20q^{19} + 4q^{21} + 16q^{22} - 10q^{23} + 32q^{24} + 18q^{25} - 24q^{26} + 4q^{27} + 18q^{28} - 26q^{30} + 48q^{32} + 18q^{33} + 2q^{34} + 40q^{35} + 36q^{36} - 4q^{37} - 8q^{38} + 4q^{39} - 16q^{40} + 10q^{41} + 40q^{42} + 10q^{43} - 36q^{44} + 4q^{46} - 40q^{47} - 56q^{48} + 18q^{49} + 36q^{50} - 30q^{52} - 10q^{53} - 48q^{54} - 10q^{55} - 16q^{59} + 28q^{60} - 16q^{61} - 44q^{62} - 36q^{63} + 20q^{64} - 14q^{65} - 32q^{66} + 18q^{67} + 22q^{68} - 16q^{69} - 12q^{70} - 16q^{71} + 4q^{72} + 18q^{74} - 38q^{75} - 64q^{76} - 28q^{77} + 68q^{78} - 2q^{80} - 14q^{81} + 56q^{82} + 48q^{83} - 40q^{84} - 26q^{85} + 60q^{86} - 34q^{87} + 82q^{88} - 6q^{89} + 46q^{90} + 8q^{91} - 8q^{92} + 32q^{93} - 48q^{94} - 26q^{95} + 56q^{96} + 66q^{97} - 30q^{98} + 60q^{99} + O(q^{100}) \)

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.t.a \(20\) \(0.519\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-6\) \(-2\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)