Properties

Label 65.2.c
Level 65
Weight 2
Character orbit c
Rep. character \(\chi_{65}(51,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 14
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 65 = 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 65.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
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

\( 6q - 4q^{3} - 10q^{4} + 6q^{9} + O(q^{10}) \) \( 6q - 4q^{3} - 10q^{4} + 6q^{9} + 2q^{10} - 8q^{13} + 8q^{14} + 10q^{16} + 8q^{17} - 24q^{22} + 16q^{23} - 6q^{25} + 14q^{26} - 28q^{27} - 4q^{29} + 20q^{30} - 4q^{35} - 34q^{36} - 20q^{38} - 16q^{39} - 6q^{40} + 44q^{42} + 24q^{43} + 36q^{48} + 2q^{49} + 8q^{51} + 20q^{52} + 12q^{53} - 12q^{55} - 48q^{56} - 12q^{61} + 8q^{62} + 30q^{64} + 2q^{65} + 24q^{66} - 88q^{68} - 32q^{69} + 20q^{74} + 4q^{75} + 36q^{77} - 52q^{78} + 24q^{79} + 30q^{81} - 28q^{82} - 4q^{87} + 60q^{88} - 34q^{90} + 32q^{91} - 20q^{92} - 8q^{94} + 16q^{95} + O(q^{100}) \)

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.c.a \(6\) \(0.519\) 6.0.5089536.1 None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)