Properties

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

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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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(65, [\chi])\) into newform subspaces

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 \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+iq^{3}-q^{4}+(1-i)q^{5}+iq^{6}+\cdots\)