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Properties

Label 520.2.cm
Level $520$
Weight $2$
Character orbit 520.cm
Rep. character $\chi_{520}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.cm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 520 \)
Character field: \(\Q(\zeta_{12})\)
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 352 352 0
Cusp forms 320 320 0
Eisenstein series 32 32 0

Trace form

\( 320 q - 2 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{8} + O(q^{10}) \) \( 320 q - 2 q^{2} - 4 q^{3} - 4 q^{6} - 8 q^{8} + 6 q^{10} - 8 q^{11} - 4 q^{12} + 4 q^{16} - 8 q^{17} - 4 q^{18} - 30 q^{20} + 8 q^{22} - 24 q^{25} - 32 q^{26} - 40 q^{27} + 14 q^{28} + 16 q^{30} - 12 q^{32} + 20 q^{33} - 4 q^{35} - 52 q^{36} - 16 q^{38} - 4 q^{40} - 8 q^{41} - 36 q^{42} - 36 q^{43} - 4 q^{46} + 36 q^{48} - 30 q^{50} - 32 q^{51} - 34 q^{52} + 12 q^{56} - 40 q^{57} + 30 q^{58} - 72 q^{60} + 40 q^{62} - 32 q^{66} - 4 q^{67} + 8 q^{68} - 52 q^{70} + 2 q^{72} - 56 q^{73} - 4 q^{75} - 4 q^{76} - 80 q^{78} + 44 q^{80} + 88 q^{81} - 42 q^{82} + 64 q^{83} + 120 q^{86} - 26 q^{88} - 68 q^{90} - 80 q^{91} - 44 q^{92} + 160 q^{96} - 12 q^{97} - 118 q^{98} + O(q^{100}) \)

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.cm.a 520.cm 520.bm $320$ $4.152$ None \(-2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$