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Properties

Label 528.2.bv
Level $528$
Weight $2$
Character orbit 528.bv
Rep. character $\chi_{528}(19,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $384$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 528.bv (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 176 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(528, [\chi])\).

Total New Old
Modular forms 800 384 416
Cusp forms 736 384 352
Eisenstein series 64 0 64

Trace form

\( 384 q + 8 q^{4} + O(q^{10}) \) \( 384 q + 8 q^{4} - 8 q^{11} + 16 q^{12} - 4 q^{14} - 8 q^{16} - 20 q^{18} + 16 q^{20} + 60 q^{22} - 32 q^{23} - 60 q^{26} + 40 q^{30} - 40 q^{34} + 48 q^{37} - 56 q^{38} + 32 q^{44} + 96 q^{49} + 40 q^{52} - 48 q^{53} - 32 q^{55} + 56 q^{56} - 8 q^{58} - 32 q^{59} - 24 q^{60} - 16 q^{64} - 24 q^{66} + 16 q^{67} - 40 q^{70} - 64 q^{71} - 20 q^{72} - 100 q^{74} - 48 q^{75} - 16 q^{77} - 72 q^{78} - 92 q^{80} + 96 q^{81} - 20 q^{82} + 200 q^{83} - 120 q^{84} - 112 q^{86} - 120 q^{88} - 40 q^{90} - 104 q^{91} - 88 q^{92} - 260 q^{94} - 100 q^{96} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(528, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
528.2.bv.a 528.bv 176.x $384$ $4.216$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(528, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)