Properties

Label 520.2.bz
Level $520$
Weight $2$
Character orbit 520.bz
Rep. character $\chi_{520}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
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.bz (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 184 40 144
Cusp forms 152 40 112
Eisenstein series 32 0 32

Trace form

\( 40 q + 16 q^{9} + O(q^{10}) \) \( 40 q + 16 q^{9} + 6 q^{11} + 6 q^{19} + 2 q^{25} - 10 q^{29} + 6 q^{35} + 24 q^{39} + 6 q^{41} + 15 q^{45} - 6 q^{49} - 48 q^{51} + 12 q^{55} + 2 q^{61} + 23 q^{65} + 24 q^{69} - 36 q^{71} + 12 q^{75} - 56 q^{79} + 28 q^{81} + 45 q^{85} - 18 q^{89} - 70 q^{91} + 8 q^{95} + O(q^{100}) \)

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.bz.a 520.bz 65.l $20$ $4.152$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(-\beta _{3}-\beta _{7})q^{5}+\cdots\)
520.2.bz.b 520.bz 65.l $20$ $4.152$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{7})q^{5}+(2\beta _{6}+\beta _{8}+\cdots)q^{7}+\cdots\)

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

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