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Properties

Label 520.2.g
Level $520$
Weight $2$
Character orbit 520.g
Rep. character $\chi_{520}(261,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $2$
Sturm bound $168$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 88 48 40
Cusp forms 80 48 32
Eisenstein series 8 0 8

Trace form

\( 48 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 48 q^{9} + O(q^{10}) \) \( 48 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} - 48 q^{9} - 4 q^{10} + 20 q^{12} + 16 q^{14} - 8 q^{15} - 24 q^{16} - 40 q^{18} + 16 q^{22} - 16 q^{23} - 24 q^{24} - 48 q^{25} + 20 q^{28} + 16 q^{31} - 16 q^{32} - 16 q^{33} + 12 q^{34} + 24 q^{36} + 20 q^{38} + 16 q^{40} + 16 q^{41} + 4 q^{42} - 44 q^{44} + 12 q^{46} - 40 q^{47} + 24 q^{48} + 48 q^{49} - 4 q^{50} - 68 q^{54} - 24 q^{56} + 16 q^{57} - 44 q^{58} - 24 q^{60} - 28 q^{62} + 40 q^{63} - 16 q^{66} + 36 q^{68} + 24 q^{70} + 16 q^{71} + 24 q^{72} + 40 q^{74} + 40 q^{76} + 20 q^{78} + 64 q^{79} + 48 q^{81} + 60 q^{82} - 76 q^{84} + 60 q^{88} - 16 q^{89} + 16 q^{90} - 28 q^{92} - 24 q^{94} - 36 q^{96} - 20 q^{98} + O(q^{100}) \)

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.g.a 520.g 8.b $24$ $4.152$ None \(2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$
520.2.g.b 520.g 8.b $24$ $4.152$ None \(2\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)