Properties

Label 520.2.ca
Level $520$
Weight $2$
Character orbit 520.ca
Rep. character $\chi_{520}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Newform subspaces $2$
Sturm bound $168$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 520.ca (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 176 112 64
Cusp forms 160 112 48
Eisenstein series 16 0 16

Trace form

\( 112 q - 18 q^{6} + 56 q^{9} + O(q^{10}) \) \( 112 q - 18 q^{6} + 56 q^{9} + 12 q^{12} - 8 q^{14} + 4 q^{16} + 12 q^{20} - 12 q^{22} + 24 q^{23} + 24 q^{24} + 112 q^{25} - 26 q^{26} - 6 q^{28} - 8 q^{30} - 30 q^{32} - 6 q^{36} - 48 q^{39} - 32 q^{42} - 30 q^{46} - 48 q^{48} + 40 q^{49} - 46 q^{52} - 54 q^{54} - 16 q^{55} + 38 q^{56} - 48 q^{58} + 8 q^{62} - 60 q^{64} + 28 q^{66} - 18 q^{68} - 132 q^{72} + 68 q^{74} - 108 q^{76} + 108 q^{78} + 24 q^{80} - 56 q^{81} - 30 q^{84} - 72 q^{87} + 22 q^{88} + 36 q^{90} - 36 q^{92} + 2 q^{94} - 32 q^{95} + 48 q^{97} + 84 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(520, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
520.2.ca.a 520.ca 104.s $56$ $4.152$ None 520.2.ca.a \(0\) \(0\) \(-56\) \(0\) $\mathrm{SU}(2)[C_{6}]$
520.2.ca.b 520.ca 104.s $56$ $4.152$ None 520.2.ca.a \(0\) \(0\) \(56\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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