Properties

Label 65.2.d
Level 65
Weight 2
Character orbit d
Rep. character \(\chi_{65}(64,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 14
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 4q^{4} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{4} - 4q^{9} + 4q^{10} - 4q^{16} - 12q^{25} - 12q^{26} + 24q^{29} + 16q^{30} + 4q^{36} + 16q^{39} - 12q^{40} - 28q^{49} - 16q^{55} + 24q^{61} + 28q^{64} - 12q^{65} + 16q^{66} - 48q^{69} - 24q^{74} + 32q^{75} - 44q^{81} - 4q^{90} + 32q^{94} + 48q^{95} + O(q^{100}) \)

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