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Properties

Label 520.2.bj
Level $520$
Weight $2$
Character orbit 520.bj
Rep. character $\chi_{520}(213,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $160$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.bj (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 176 176 0
Cusp forms 160 160 0
Eisenstein series 16 16 0

Trace form

\( 160 q - 4 q^{6} - 8 q^{7} + O(q^{10}) \) \( 160 q - 4 q^{6} - 8 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 8 q^{16} - 8 q^{17} + 16 q^{18} + 16 q^{20} - 32 q^{22} - 28 q^{24} + 12 q^{26} - 20 q^{28} + 8 q^{30} - 8 q^{31} + 16 q^{34} - 8 q^{38} + 28 q^{40} - 8 q^{41} - 16 q^{42} - 24 q^{44} - 4 q^{46} - 8 q^{47} + 8 q^{48} + 112 q^{49} - 32 q^{52} - 12 q^{54} - 8 q^{55} - 60 q^{58} - 44 q^{60} - 28 q^{62} + 32 q^{65} - 8 q^{66} - 72 q^{68} - 16 q^{70} - 40 q^{71} + 16 q^{72} + 28 q^{76} + 60 q^{78} + 28 q^{80} - 112 q^{81} + 16 q^{82} + 20 q^{84} + 24 q^{86} - 32 q^{87} - 64 q^{88} + 44 q^{90} - 20 q^{92} + 48 q^{96} + O(q^{100}) \)

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.bj.a 520.bj 520.aj $160$ $4.152$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$