Properties

Label 520.2.f
Level $520$
Weight $2$
Character orbit 520.f
Rep. character $\chi_{520}(129,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(520, [\chi])\).

Total New Old
Modular forms 92 20 72
Cusp forms 76 20 56
Eisenstein series 16 0 16

Trace form

\( 20 q - 16 q^{9} + O(q^{10}) \) \( 20 q - 16 q^{9} - 2 q^{25} + 16 q^{29} - 6 q^{35} - 24 q^{39} + 24 q^{49} - 60 q^{51} + 24 q^{55} - 32 q^{61} - 14 q^{65} - 24 q^{69} + 42 q^{75} + 56 q^{79} + 44 q^{81} + 4 q^{91} - 20 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
520.2.f.a 520.f 65.d $10$ $4.152$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
520.2.f.b 520.f 65.d $10$ $4.152$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-\beta _{6}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)