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Properties

Label 520.2.bu
Level $520$
Weight $2$
Character orbit 520.bu
Rep. character $\chi_{520}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.bu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
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 28 156
Cusp forms 152 28 124
Eisenstein series 32 0 32

Trace form

\( 28 q - 4 q^{3} + 12 q^{7} - 14 q^{9} + O(q^{10}) \) \( 28 q - 4 q^{3} + 12 q^{7} - 14 q^{9} - 6 q^{11} - 4 q^{13} - 4 q^{17} + 6 q^{19} + 4 q^{23} - 28 q^{25} + 32 q^{27} - 4 q^{29} + 24 q^{33} - 10 q^{35} + 20 q^{39} - 12 q^{43} + 20 q^{49} - 40 q^{51} - 64 q^{53} - 4 q^{55} - 36 q^{59} + 16 q^{61} - 96 q^{63} + 6 q^{65} + 12 q^{67} + 44 q^{69} + 72 q^{71} + 4 q^{75} + 96 q^{77} + 24 q^{79} - 14 q^{81} - 4 q^{87} + 54 q^{89} + 54 q^{91} - 108 q^{93} - 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bu.a 520.bu 13.e $12$ $4.152$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{3}-\beta _{5}q^{5}+(-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
520.2.bu.b 520.bu 13.e $16$ $4.152$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{3}+(\beta _{9}-\beta _{10})q^{5}+(\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)