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Properties

Label 65.2.f
Level 65
Weight 2
Character orbit f
Rep. character \(\chi_{65}(18,\cdot)\)
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.f (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

\( 10q - 4q^{3} - 6q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + O(q^{10}) \) \( 10q - 4q^{3} - 6q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + 8q^{10} + 4q^{11} + 10q^{13} - 4q^{15} - 10q^{16} + 14q^{17} + 18q^{18} - 4q^{19} - 6q^{20} - 16q^{21} + 8q^{22} - 20q^{23} + 4q^{24} - 6q^{25} + 12q^{26} + 20q^{27} - 12q^{28} - 16q^{30} + 12q^{31} - 2q^{34} - 16q^{35} - 44q^{37} + 8q^{38} - 4q^{39} + 28q^{40} + 2q^{41} + 20q^{42} - 4q^{43} - 12q^{44} + 24q^{45} + 8q^{46} + 28q^{47} - 16q^{48} + 18q^{49} + 36q^{50} - 42q^{52} - 14q^{53} + 12q^{54} + 16q^{55} + 24q^{58} - 8q^{59} - 16q^{60} - 8q^{61} - 40q^{62} + 34q^{64} + 2q^{65} - 40q^{66} + 2q^{68} - 8q^{69} - 72q^{70} - 8q^{71} - 22q^{72} + 44q^{75} + 16q^{76} - 20q^{77} + 4q^{78} - 22q^{80} - 10q^{81} + 34q^{82} + 60q^{83} - 20q^{84} + 38q^{85} - 48q^{86} + 16q^{87} - 16q^{88} + 18q^{89} - 10q^{90} + 28q^{91} + 44q^{92} - 20q^{93} - 28q^{95} + 40q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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